You can be the organizer without being the one who does everything.

Organising a thing and carrying a thing are separate jobs, and whoever starts the group chat usually ends up with both. It happens because handing out tasks feels like an imposition while quietly doing them feels easier. A month later you are resentful and everybody else thinks it runs itself. Delegating is part of organising, not a failure of it.

Next time you set something up, give three specific jobs away before you take any: who brings what, who books, who messages the group. Ask directly and name the person. People almost always say yes to a specific request.