I had this exact issue with both my desktop and server. Anytime I put any sort of load on the outbound connection, the wifi would cut out. After switching to the iwd backend, I haven’t had any issues.

You could try switching your wifi backend to iwd instead of wpa_supplicant.

If you’re using NetworkManager, then create the file /etc/NetworkManager/conf.d/wifi_backend.conf, and add the following configuration:

[device]
wifi.backend=iwd