Additional chat-related features and issues within Microsoft Teams for Education
Check out this fairly new feature, and see if it might help.
https://teamsinsider-dev.azurewebsites.net/blog/people-app-in-teams-free/
This is the people app that's currently only available for Teams Insider users.
To opt into Insider, go to your Teams app settings > Teams Insider program. Opt in there. It can take perhaps half an hour for your Insider status to kick in, look for the Update gray button on the upper right when it appears, then click on it to update and restart. Then see if you have the People tab on the left. It worked for me, but I migrated from Skype to Teams before Skype retired in May.