All, I don't know what I've done but now it is working on both Android and Fedora. I thank everybody who has helped correcting me or confirming that what I was doing was right.

On Fedora, what was key was - apparently - clicking on Reset > Reset in the L2TP configuration, as if something "dirty" was hanging around in the configuration.

Only one issue remains open. I cannot start the VPN on Fedora if the VPN is already running on the Android phone I am using as hotspot. I can do the other way round: I can start the VPN on Android after I started it on the Fedora laptop. I know that by design the Android hotspot does not allow to share the VPN... but why wouldn't the Fedora VPN client be able to start then?