The main problem in my case was Trend Micro antivirus installed on the endpoint. MacBook without Trend Micro worked fine. Update to macOS 13.1 did not resolve my problem - mac stuck on login screen.
After some tests I found out the issue in the MDM profile with payloadtype com.apple.MCX.
After remove of the configuration profile for TimeZone setup, user can logon without stuck.
Example of my TimeZone configuration profile.
<dict>
<key>PayloadType</key>
<string>com.apple.MCX</string>
<key>PayloadDisplayName</key>
<string>Time Server</string>
<key>PayloadVersion</key>
<integer>1</integer>
<key>timeServer</key>
<string>time.apple.com</string>
<key>timeZone</key>
<string>Europe/Prague</string>
<key>PayloadUUID</key>
<string>0ECAFFC4-A0AD-4124-B3ED-XXXX</string>
<key>PayloadIdentifier</key>
<string>com.apple.MCX.0ECAFFC4-A0AD-4124-B3ED-XXXX</string>
</dict>
BUT, you can use one of this steps as workaround:
Before reboot disable wifi connection (turn OFF toggle on the wifi adapter)
Try logon to Mac on the place, where Mac cannot automaticly connect to known wifi SSID (for examle turn off wifi AP at home).