Hello!
I installed Ubuntu Budgie and I have an issue with the lock screen.
When the computer is idle and I press a key I have this screen:
The circle moves as I type the password. Is it supposed to look like this?
Yes - this is the default lock screen the distro ships with - its called swaylock.
You basically just type your password and press enter to unlock.
If you want the traditional looking lock screen then install the package “gtklock” - logout and login.
Can you somehow login as a different user in a lock screen?
Not directly available under wayland. Once the locker is visible it owns the whole session (the active seat). This is a feature of the wayland security mechanism.
The only real way is to control end-to-end the whole login manager - desktop session - lock screen mechanism. That is some-thing way beyond budgie which uses a separate login manager (sddm) - its desktop session over the top of a wlroots compositor such as labwc - and a separate locker like swaylock / gtklock.
Other workaround could be to use logind to activate another session before the lock screen is invoked. Possibly using another TTY and activating (dbus-run-session type mechanism) budgie.
Would be interesting to explore further I would imagine.