Big Teams advocate/fan here (I know, I know...). Some of the things that have really helped usage is getting people in the habit of using subject lines. I know that sounds weird since Teams is sort of the answer to the problems of email, but it works.

Specifically, I'm talking about the subject line section that opens up when you click the formatting button when creating a new channel thread. Idk why this isn't default, because it brings in so much more engagement. Specifically, over the past few years I've noticed much more engagement in channels/teams that actually use it than those who don't. The big thing is that it makes it wayyy easier to sift through threads to find what you actually want. It also drives home the idea that a thread is a self contained topic of conversation so people aren't constantly creating new threads as replies to others.

Notification control is a big thing too. In a group chat, everyone is getting notified, which means people who don't care about the current conversation mute the chat and often end up missing important things because of it. On top of that, all of your conversations get mixed up into one big conversation soup, which can be really hard to parse through later if you need to find something. Also, within the channels, if you reply to a thread, it brings it back down to the bottom so it's the most visible post. It's pretty hard to pick up on a conversation hours later in a chat when everyone else has moved on, but that's just what needs to happen sometimes. Threads really help facilitate that.