The world is set up like a normal comedy sitcom. Problems arise and get solved in 20 minutes and everything is fixed and resets back to the default at the end of the episode.
But one of the characters ages and remembers what's happened. They eventually catch on that nobody else remembers and that they are aging while everybody around them stays static and accepts the main character’s aging as things have always been. They have repeated plots where the specifics change but the general episode has a repeated structure.
Think like the Simpsons and everything stays static for everybody except Lisa. Bart and Maggie are perpetual kids and stay the same, but Lisa is aging and remembers the formulaic plots and adventures the family and town have.
Upon the lead figuring it out, it would start like Groundhog Day, where you know your actions don't have consequences so you can experiment and try things out. You can burn down a building because you know that by next episode, the building will be back or nobody will acknowledge that a building was ever there. Unlike Groundhog Day, you have to protect yourself. Since the main character isn’t static, they still can’t do anything super dangerous or hurt themselves.
I think the “sitcom” version of a time loop has more of an inherent sadness than a regular time loop. Groundhog Day still has possibility and a goal. In Groundhog Day, you can do the perfect run of the day. You can get everything right, have a good day yourself, and make everybody around you happy. But in the sitcom, everything is meaningless because the world of a sitcom that’s been on for dozens of seasons doesn’t make meaningful changes. You can have that perfect day but no matter how happy you make yourself or everybody, they're back to default next episode and a new plot begins. The same exact day isn't repeating so you can't learn the loop; it's that time advances but keeps defaulting to a different but meaningless default state. It doesn't matter if you grow as a person or help people because it just gets wiped out and the previous adventure gets ignored.
There's also a more impending and grander doom to the sitcom version. Eventually, the child character would age up into a teen then adult then equaling and finally surpassing their parents in age. What happens when they finally die? Does the show go on the same as always, just without you and your role never mattered?
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This was definitely an idea born from reflecting on being sad at work. It wasn't just that I didn't like being at work, it was that my job had the potential to be good but it wasn't and nothing I worked on mattered because a company in its child-like state would eventually grow tired of the project and move to the next shiny object. I was assigning tasks to team members and one of them asked me in private if he should care about the tasks or were they just flavor of the week. And “flavor of the week” was the answer because in a few days or weeks, we trashed that project and moved over to something else, so all those tasks wound up being meaningless and thrown away. It would have been a waste of everybody’s time to really try their best or invest themselves in what I was asking them to do. The company could hold retros and postmortems but it didn't matter what anybody said because, after the meeting, the slate would be wiped clean and you'd be back at default for the next project. I kept getting deja vu and time would kind of run together because I'd find myself in a conversation and then remember that we had that same conversation a few months ago. The days were different so I could never do a perfect run of them, but everything was stagnant so I felt like I was stuck in that loop.