Update: After much more digging, I finally found an answer: Microsoft must've changed something on their end that altered authentication. If multiplayer is showing as disabled for you, you need to follow the steps listed here to get your access token from a profile that authenticates normally outside the dev environment:
https://gist.github.com/50ap5ud5/beebcf056cbdd3c922cc8993689428f4#minecraft-authentication-in-dev-environments
In my case it turned out I just needed my access token, it may or may not still need the UUID. The guide is older so I don't know how many versions it will hold up in, but in my case this did seem to be what Eclipse was looking for.