Can you check the settings under Settings / Bluetooth and Devices /Print Server Properties on the security tab?
On my (Windows 11 Pro) system guest access is denied - you may need to change this through the Advanced button.
View attachment 96993
(I'm not sure if Windows 11 Home even supports local accounts anymore, which would be the way described earlier with identical, password protected user accounts on each device, same name, same password for accessing the shared printer - and even this may require additional work to disable some checkups. So guest access might be the solution.)
Or you could try to use the same Microsoft account for login on the Print Server PC and the Windows 11 machine.
Best greetings from Germany
Olaf