There is definitely something that is not working as expected. In the first screenshot, there should be the ability to select a database under the "Database" header on the left side panel. After selecting the database a corresponding list of data tables should be made available and can be dragged into the view.
Once the connection is established, you can move to the first sheet, and begin creating your visuals.
Hope this helps!
Have you tried the 'edit connection' option for this MySQL data source in Tableau Server?
Press the 'test connection' button to test the if can connect or not.
Also, you may edit port there.
Linux Server has no problem connecting MySQL.
I suspect issue is due to the network configuration to MySQL different between your Tableau Desktop machine and the Server machine.
Hope it helps.