Pretty much every streaming app I use (not just on AppleTV) has a hard time remembering where I left off. I now have the habit of skipping through the credits and letting the app play the last 8 seconds and close the episode itself, in the perhaps misguided hope that then it will remember I've played the episode.

Exactly. The issue of marking as played is not unique to Peacock, but Peacock’s lag makes it take even longer to get confirmation that some of the other apps I’ve used. Netflix has the same issue and some lag to it, but it’s less lag.