I could swear I read somewhere about an app where you share a severely scaled down (or maybe slightly blurred?) version of your desktop throughout the entire workday.

I would allow your mate to sense the situation when you could be more available for chatting/socializing/etc.

My google-fu is failing me, I think I saw it ~2019 but cannot find anything now.

And of course the focusmate seems to be still a thing: https://news.ycombinator.com/item?id=21352305