I'm tired of holding everyone's conflict and never taking a side, what do I do?

You can bring almost any two sides to the table, and after years of holding other people's conflict you are weary of never getting to take a side of your own. That weariness makes sense. Neutrality is demanding work. You absorb everyone's heat and give back calm, over and over, and never get the release of simply being for something. That empties a person out in a way few people see. The neutrality your work requires is a real skill and a real gift, but it was never meant to be the whole of who you are. In the room, you hold the middle; that is the job. Outside it, you are allowed to have strong opinions, to be partial, to care loudly about things and take a side without apology. The two do not cancel each other out. So give yourself somewhere to not be neutral. Causes you back openly, people you are fully on the side of, opinions you say plainly instead of balancing. Let yourself be partisan in the parts of life that are not your work. You spend your days making room for everyone else's position. Make some room, off the clock, for having one of your own.