You should not use gMail to access federal/state resources, but "state mail". Like DigiD in Netherlands, DataBox in Czech Republic. Both are state ran, associated with your identity. Lost password can be unlocked by going physically to office.
A tricky question. Many schools in other EU countries are using Google Office Suite and Google Classroom. Is that also the same issue? My kids reports are published via Google Docs.
How about Microsoft's Office 365? Do they have data centers in EU? Or is that the same issue? Because then we also have fully Microsoft based school including extended Teams usage.
Basically how do you want to have any cloud based app running in EU when most of the providers don't have data centers here in EU?
It got modernized ;-)