and the phone is on the screen with “fastboot mode written”, asking me to choose wether to start, restart bootloader,go to recovery mode or power off"
Nothing else happens whatever I choose (device powers on to E/OS)
While the FP3 is in fastboot mode and connected via USB you should force a search for windows updates. This should then suggest to install optional updates where you can then select to install additional drivers.
Memories of the past perhaps, when it was the other way around and Linux acting up on ADB and fastboot stuff could almost always be worked around by trying it on Windows?
That was before fastboot needed installing a driver on Windows, though … ah, good times, grandpa telling stories from the war .