Searching for games that fit, I am reminded that there’s a frustrating number of games that have a difficult mode, but refuse to let you play it until you’ve beaten the game on an easier setting (sometimes more than once!) It might be possible to work around that by copying someone’s save file.
This list isn’t super filtered, but here’s some games that seem vaguely in line with your request:
Solar Settlers Short strategy game with somewhat-risky exploration, pointed resource optimization, and exponential growth (if you play well). Advertises a 10-minute playtime, but I think (this was years ago) that my games lasted more like 1-2 hours; I expect this is partly because I’m slow but partly because the better you play the more stuff you need to manage.
I think (66% confidence) the difference between difficulty levels is just how many points you need to count as a “win”, and that you can finish the game even if you reach that threshold, so you could maybe tune the difficulty of the exercise by asking for a different score than what the game says. (Though IIRC there’s a regular play mode, and a skill-calibration mode, and I think only one of those lets you keep playing after you reach the target score, and I don’t remember which.)
Defense of the Oasis Explore the map and invest your followers into exploiting various terrain features to prepare for a barbarian invasion. Short levels escalate in difficulty, play until you die. Starts easy, but you could probably pick some number of stages (or some score threshold) that would be challenging.
Various Roguelike Deckbuilders Those I’ve played tend to be a bit longer than you asked for but not hugely so. The default difficulty is often hard for players unfamiliar with these types of games (but easy for veterans), and there’s often harder unlockable difficulties. There’s typically “rules-based” hidden information in the form of not knowing the full set of cards and challenges that exist in the game, but rarely any “gamestate-based” hidden information.
You mentioned Luck be a Landlord, which is sort of on the edge of this category; compared to most I’ve played, it’s faster, simpler and has no hand management. Another game I’ve played that’s on the edge of this category is Crop Rotation, which is more of a tableau-builder than a deckbuilder since all your cards are available at once (there’s still luck, but mostly in what cards are offered in drafts).
Into the Breach A tactical battle game where the enemies need to charge up their attacks and you can make them miss (or even hit each other) by moving things around, and you gradually upgrade over a series of short missions. I think this one actually lets you play on hard mode from the start, but I don’t remember for sure. Not much in the way of hidden info.
You can vary the game length by choosing to play 2, 3, or 4 islands before doing the finale.
ETA: Tyrant’s Blessing has very similar gameplay and is much less likely to have already been played by your audience (though it’s so similar that I’d expect a lot of skill transfer, and I’m uncertain about the difficulty and playtime).
Renowned Explorers: International Society This is likely too long, but allegedly there are players who can finish a run in under 2 hours. It’s basically a combination of story events and turn-based tactical battles, with periodic breaks to spend your accumulated resources on upgrades. There’s a mechanic where you can do extra events for more resources at the cost of taking penalties that make the fights more difficult.
It’s not that hard, but if you restrict yourself to only choosing expeditions from the highest-unlocked difficulty rating then most players probably won’t win their first run. Experience at tactical skirmish games may provide a significant advantage.
ETA: Thought of a couple more, although these seem even less promising to me:
Farm Keeper Turn-based economic strategy where you need to make escalating rent payments. The starting difficulty is almost certainly too low for you, and once again, it only unlocks higher difficulties one at a time as you win. Meeting various conditions while playing also permanently unlocks “secret tiles” that make all future runs easier by giving you more (and typically better) options. Harder modes are also longer and may exceed the playtime you want. So setting up an appropriate challenge might be painful.
It’s also somewhat unfair as a one-shot exercise, because as you play you get access to new tiles that substantially alter the optimal layout, but you can’t move your existing tiles and you can’t see the late-game tiles in advance, so you can end up getting punished for having done a good job of optimizing the variables that you knew about. (Though conceivably this teaches something about flexibility?)
Lueur and the Dim Settlers This game actually isn’t even out yet, but there’s a free demo. The demo is certainly too easy for your purposes. But it’s a relatively short turn-based survival strategy game where exploration plays an important role. (Note: I have only a vague memory of how long this took to play.)
I think there were some simple action-based mini-games, too, so it’s not pure strategy.
ETA Again: If unknown information is not such a priority, one could also look at some solo-friendly strategy board games—several of which have digital versions, such as Spirit Island, Aeon’s End, or One Deck Dungeon.
Searching for games that fit, I am reminded that there’s a frustrating number of games that have a difficult mode, but refuse to let you play it until you’ve beaten the game on an easier setting (sometimes more than once!) It might be possible to work around that by copying someone’s save file.
This list isn’t super filtered, but here’s some games that seem vaguely in line with your request:
Solar Settlers
Short strategy game with somewhat-risky exploration, pointed resource optimization, and exponential growth (if you play well). Advertises a 10-minute playtime, but I think (this was years ago) that my games lasted more like 1-2 hours; I expect this is partly because I’m slow but partly because the better you play the more stuff you need to manage.
I think (66% confidence) the difference between difficulty levels is just how many points you need to count as a “win”, and that you can finish the game even if you reach that threshold, so you could maybe tune the difficulty of the exercise by asking for a different score than what the game says. (Though IIRC there’s a regular play mode, and a skill-calibration mode, and I think only one of those lets you keep playing after you reach the target score, and I don’t remember which.)
Defense of the Oasis
Explore the map and invest your followers into exploiting various terrain features to prepare for a barbarian invasion. Short levels escalate in difficulty, play until you die. Starts easy, but you could probably pick some number of stages (or some score threshold) that would be challenging.
Various Roguelike Deckbuilders
Those I’ve played tend to be a bit longer than you asked for but not hugely so. The default difficulty is often hard for players unfamiliar with these types of games (but easy for veterans), and there’s often harder unlockable difficulties. There’s typically “rules-based” hidden information in the form of not knowing the full set of cards and challenges that exist in the game, but rarely any “gamestate-based” hidden information.
The best-known is Slay the Spire. I think the original and the hardest I’ve played is Dream Quest, but it’s very luck-dependent. Some others that have informed my impressions of this subgenre include Monster Train and Roguebook. There’s a zillion other ones nowadays.
You mentioned Luck be a Landlord, which is sort of on the edge of this category; compared to most I’ve played, it’s faster, simpler and has no hand management. Another game I’ve played that’s on the edge of this category is Crop Rotation, which is more of a tableau-builder than a deckbuilder since all your cards are available at once (there’s still luck, but mostly in what cards are offered in drafts).
Into the Breach
A tactical battle game where the enemies need to charge up their attacks and you can make them miss (or even hit each other) by moving things around, and you gradually upgrade over a series of short missions. I think this one actually lets you play on hard mode from the start, but I don’t remember for sure. Not much in the way of hidden info.
You can vary the game length by choosing to play 2, 3, or 4 islands before doing the finale.
ETA: Tyrant’s Blessing has very similar gameplay and is much less likely to have already been played by your audience (though it’s so similar that I’d expect a lot of skill transfer, and I’m uncertain about the difficulty and playtime).
Renowned Explorers: International Society
This is likely too long, but allegedly there are players who can finish a run in under 2 hours. It’s basically a combination of story events and turn-based tactical battles, with periodic breaks to spend your accumulated resources on upgrades. There’s a mechanic where you can do extra events for more resources at the cost of taking penalties that make the fights more difficult.
It’s not that hard, but if you restrict yourself to only choosing expeditions from the highest-unlocked difficulty rating then most players probably won’t win their first run. Experience at tactical skirmish games may provide a significant advantage.
ETA: Thought of a couple more, although these seem even less promising to me:
Farm Keeper
Turn-based economic strategy where you need to make escalating rent payments. The starting difficulty is almost certainly too low for you, and once again, it only unlocks higher difficulties one at a time as you win. Meeting various conditions while playing also permanently unlocks “secret tiles” that make all future runs easier by giving you more (and typically better) options. Harder modes are also longer and may exceed the playtime you want. So setting up an appropriate challenge might be painful.
It’s also somewhat unfair as a one-shot exercise, because as you play you get access to new tiles that substantially alter the optimal layout, but you can’t move your existing tiles and you can’t see the late-game tiles in advance, so you can end up getting punished for having done a good job of optimizing the variables that you knew about. (Though conceivably this teaches something about flexibility?)
Lueur and the Dim Settlers
This game actually isn’t even out yet, but there’s a free demo. The demo is certainly too easy for your purposes. But it’s a relatively short turn-based survival strategy game where exploration plays an important role. (Note: I have only a vague memory of how long this took to play.)
I think there were some simple action-based mini-games, too, so it’s not pure strategy.
ETA Again: If unknown information is not such a priority, one could also look at some solo-friendly strategy board games—several of which have digital versions, such as Spirit Island, Aeon’s End, or One Deck Dungeon.
+1 for Into the Breach