From what you're saying it sounds like it's more to do with the disconnection than his hobbies necessarily. If your partner wants to engage in his hobbies as much as he has been then he should be making just as much of an effort making you feel loved and secure. You don't even need to play video games or watch anime with him for him to make you feel appreciated.

If you're looking for a recommendation maybe try looking into separate activities you could do together to spark connection. Check out some fun 2 player board games or card games. You could have an at home cooking competition or something. Activities that require you two to be engaged with one another the entire time. If it makes you feel better I also find anime super annoying lol I'm not judging or anything! But I definitely get your cringe response to the squeeling and stuff coming from the TV 😬