Meanwhile it feels like half my colleagues don't understand the difference between starting a new Teams conversation ("thread" in Slack), or replying to an existing one. And there's no way to move a message that was posted in the wrong conversation. AFAIK it's the same with Slack threads.

Getting people to post in the "correct" channel faces similar challenges.

Imagine the chaos that would result if we ran everything through Teams.

Prescriptivism rarely improves communication, so consider changing your expectation rather than policing others.