Cant see the database

You are absolutely right, the screenshots that are in our guide refer to Local by Flywheel (version 3.3.0) which is the last official release and it appears that your student is using Local Lightning (which is in beta). There are a couple options here.

The first is that there is a new beta available that we recommend upgrading to (5.0.7):
https://localbyflywheel.com/community/t/5-0-7-beta/15063

Or, since documentation will reflect the official release, you can direct your student to use version 3.3.0:

If you opt to install version 3.3.0 keep in mind that these run in different environments and therefore sites that exist in the beta will not be present in version 3.3.0.