I think that using the word “valuing” adds back in confusion that this trichotomy is trying to remove. Wanting is the axis of urgency to act or not act, liking is the axis of feeling enjoyment or suffering, and approving is the axis of feeling morally elevated or disgusted. These are independent axes that can exist simultaneously regardless of time, and which are only made more vague by lumping them together as “valuing”.
(Notably, one’s experience can be placed simultaneously on all three axes: it is not necessary for these experiences to be separated in time. You can approve or disapprove beforehand and during, not just after. You can want while doing, as well as beforehand.)
My thought on this is probably biased by my work helping people with akrasia, procrastination, etc., but in my experience the difference in work vs. play seems to be because of how our brains process costs vs. rewards. When you are doing something as a hobby, the reward is immediate and the cost or threat is low, because you want to do it and nothing bad happens if it doesn’t work out.
In contrast, when you have to do a specific thing at a specific time (e.g. because it’s for work), then there is a definite cost to insufficient performance, but a sufficient performance is merely the status quo… meaning there’s no perceived reward.
In addition, exceptional performance, if repeated often enough, will raise the status quo, making your situation objectively worse!
Under such conditions, engaging with the work feels risky or costly in a way that a hobby project does not.
I personally suffered from issues with this for a very long time, which led to me blogging and then becoming a coach helping people with similar issues… and then getting stuck in akrasia for many years because I’d turned my exciting new hobby into an unmotivating profession, and didn’t notice the meta issue. :-)
Solving this type of problem is simple in principle: eliminate the threat-perception, and reset your perception of the “status quo”. But the devil is in the details because your brain wants to add any increased rewards into a new status quo, and anything that threatens to lower that standard tends to get viewed as a threat. (Including, paradoxically, any discussion of intentionally lowering one’s standards or demands for reward!)
There are techniques that address these things, but some ongoing management is required; otherwise within a few months I tend to drift back to being creatively blocked or unmotivated in relation to paid work or work that’s aimed at getting paid.