Certainly eggs are not likely to suffer at all.
It’s typically the chickens laying the eggs that people are concerned about. And maybe to a lesser extent the male chickens of the chicken breed used for egg production. (Maybe you’re already clear on that, but I have spoken to people who were confused by veganism’s prohibition on eating animal products in addition to animals.)
They likely do not suffer in the same way people do.
It doesn’t seem safe to assume that their suffering is subjectively less bad than our suffering. Maybe it’s worse—maybe the experience of pain and fear is worse when you can only feel it and can’t think about it. Either way, I don’t see why you’d err on the side of ‘It’s an uncertain thing so lets keep doing what we’re doing and diminish the potential harms when we can’ rather than ‘It’s not that unlikely that we’re torturing these things, we should stop in all ways that don’t cost us much.’
But yes, creating vat-grown meat and/or pain-free animals should be a priority.
If Brunemeier’s PDF’s is something you can share, I’d like to read it.