This is a very fresh change and was just merged in. General is now the default category in the composer on NEW sites.
https://github.com/discourse/discourse/pull/18383
This doesn’t exist yet, but I’m open to adding it!
For existing sites I’ll have to come up with a plan on how they can get the default category feature. Right now it requires disabling the allow_uncategorized_topics, but then it will also require that the General category exists and that the hidden site setting general_category_id is set, but if admins could customize which category was the default this would make it easier for existing sites to get this functionality and possibly get it to work with uncategorized enabled still.