Emit is stuck in my household and nothing I've tried will remove him

I don't know if there's an official fix, but one option would be to play as a different household, visit, and add him to that household the way you added him to your current household.

Another option would be to choose or create a disposable household in manage households, move sims between households until all your current sims are in that household and all the sims from the disposable household are in your current household with Emit. Then you just need to move the disposable household out of your house so your current sims can move back in. Emit should be attached to the household ID, not to any specific sim or the house, so that should get rid of him.

Make sure you don't leave any personal belongings behind in the house. Before I got keepsake boxes I used to store my spellcasters' sample potions on shelves in their bedrooms, and the potions got deleted when I moved the household out of the house to attend university and then moved back after graduation.

how did you manage to add him to your household? my sim decided to start a family with him and I would like to keep him in the gameplay after the event ends