Always my problem with Tailscale and similar solutions is that I already run VPNs in my personal devices and especially with android devices, I need to switch between two VPNs, which I find a friction that I do not want. Does anybody know a solution to this?
Tailscale has some integration with Mullvad. If you have a Mullvad subscription you can use their servers as exit nodes without dropping your Tailscale connection: https://tailscale.com/kb/1258/mullvad-exit-nodes
Outside of the particular combination of Mullvad and Tailscale I don't think there is any other way apart from switching between the two.
Not elegant or performant but:
You could have a exit node that is setup only for that vpn that advertises it's routes. So connecting to tailscale gives you access to that network.
Maybe I don't understand, but the tailscale Linux clients definitely supports multiple accounts. I use that to reach multiple headscale networks and a tailscale one. No issues for me using it this way.