Wow, you just... described the problem we had on our Windows PCs that I never managed to describe

This is the correct answer. If you don't need notifications:

Make sure you enable the auto frost service in Shelter's settings, enable auto frost for WhatsApp in Shelter and replace the icon on your home screen with a Shelter shortcut.

You can also use a trustworthy VPN to route traffic from the entire work profile or only from WhatsApp.

Damn, Astrill is expensive though. Friend in China is currently happy with Mullvad + Shadowsocks. A few hiccups here and there, but it works pretty well and is fast enough for streaming, too.

They also have guides to a few more involved methods in case Shadowsocks is blocked.

First had Kodi on a RPI, but I got fed up with Kodi, partly because there are too many moving parts and partly because there's no great way to watch YouTube.

Then found Flexlauncher, which has already been suggested by someone else. Slapped Debian on the RPI and then realized that getting smooth HD YouTube video playback is impossible outside of Kodi, because of hardware (?) limitations.

At this point I decided that enough is enough and just got out the old laptop in the household no one uses anymore, same Debian + Flexlauncher combo with Stremio and Freetube. Set Debian to do auto login and start Flexlauncher automatically. Works great, but controlling with Keyboard only (and using the laptop trackpad when nothing works) gets a bit annoying. Looks like an airmouse is the way to go.