Ok, I found a very convenient 1-(double)click workaround for me (S22 Ultra, Android 14): unlock the phone remotely with a batch file! Afterwards screen sharing works normally with Phone Link or any other remote software.
It's at the edge of being viable for normies, but it's not utterly complicated once you understood the required tools. It's simply using ADB to send the PIN as key inputs to the phone, which unlocks it: "adb shell input text XXXX" (where XXXX is your PIN). By far the easiest way is to have the phone connected over USB - you just have to enable USB debugging in the developer options once and then you can send ADB commands all day long.
It's more complicated to do it over Wifi. All modern phones support Wifi debugging but it has to be enabled once every reboot. Modern Samsung phones also have a convenient quick-settings button for it. Once it's running, you have to connect once from your PC to pair it ("adb connect IP:PORT") and then you can make a simple batch script like:
@echo offpushd "Z:\platform-tools"adb connect IP:PORTadb shell input text XXXXadb disconnectpopd
If your phone requires pressing OK after entering the PIN, add "adb shell input keyevent 66". For patterns or passwords the input sequence is different, you have to do your own research..
A big inconvenience on modern Android (11+) is that the port number for ADB over Wifi randomly changes each time you turn it on, so you'd have to modify your batch file each time. At least the IP address can be fixed if you give it a fixed IP in your router settings (or a DNS name). To avoid that, you have to enable legacy Wifi ADB which uses a fixed port (5555), and the easiest way is to run the LADB app on the phone once per reboot with a startup command to enable the legacy mode (see here for more details). The rabbit hole is probably too deep for nearly everyone, but it can be done...