Hey @Razor161!
Got it working now!
I bought a USB-C Gigabit LAN Adapter with Charging Input (usually for Tablets, etc) and use this as the network interface for the pico instead of Wifi. It works flawlessly for me right now.
My PC is connected to the router via LAN (PowerLAN) anyway, I just added a switch before the PC and connected the Pico to the same switch. Wifi disabled completely. Pico has Internet, Virtual Desktop uses this connection without any complaints. No more bluescreens and VD shows stable 1200Mbit/s.
One drawback I haven’t solved yet: I don’t think the Pico is charging while in use. It does show a charging symbology but gradually discharges slowly, maybe slower than without charging, I don’t know. Charging works while the Pico is off at least. Will report if I can solve this.