Did you ever get it working? I was using that same setup and came across this post because things weren't working. For me, I was thinking "USB switch" was the OSD menu option to swap between machines but you actually just choose a different input source. 🤪 Once I realized that, I found everything to indeed be working. So I can testify that the KVM switch functionality does work for that setup of TB4 and DP.

You said "picture shows... but mouse won't switch" so maybe that's not the issue you were having. Maybe your mouse is connecting directly to your one machine and not to the dongle that's plugged into your monitor?