The Shared Libraries list on OneDrive will show libraries you frequently use. There doesn't seem to be any published definition of how to alter this list - how often you have to use something etc - but you can follow sites so that they show up when you click More Libraries:
- Open Teams, then go into the team you wish to add to your Shared Libraries.
- Go to the GeneralĀ channel, then the FilesĀ tab:
- Click on Open in SharePoint:
- Click on the star next to Not Following at the top left, to fill the star in and change it to Following:
- Now in OneDrive, when you click on More Libraries it will appear under Followed:
Now when you are trying to move or copy files from OneDrive to the shared library, you can click on Browse Sites:and it will show your followed sites as well as frequent/recent sites: