The issue is only when the phone has been booted but not unlocked yet. Once you unlock and re-lock everything works. (That’s also why you will only notice the issue after a reboot)
My solution to get rid of google gboard was to change the lock from “password” to “pin” and use a long custom pin for unlocking. Unlike passwords, for which the lock screen invokes the system keyboard, for pins, it uses its own pin entry interface (and it also does for emergency numbers and for SIM pins if the SIM is locked with a pin)
in my case, after a cold reboot, I need to enter 3 pins. The pin for the 1st SIM, the pin for the 2nd SIM, and the PIN that phone is locked with.
On standby the SIM’s don’t need unlocking, so I only enter the phone PIN.
I worked around the reduced security of having only 10 digits by chosing a really long PIN.