I use Pixel with GrapheneOS as my phone, and I just have a separate profile that only has WhatsApp installed and nothing else. It's not running in background, so it's disabled all the time, and since the profiles are completely separated, it doesn't have access to anything else I do on the phone.
When the bridge asks me to log in again or refresh a session, I simply switch to the second profile for a minute and re-log in. I've heard iIt might be possible to set up an emulator and leave it running on the server, but that felt like too much effort.