I use free streaming services (such as used to be with the old "iTunes radio tuner").
I use either a modified copy of iTunes (which will work on Sequoia), or, the little app called "Radiola".
For either of these, switching the VPN on/off will break the connection, and it will have to be re-opened "manually".
I've gotten used to it. Sometimes you just have to do, what you have to do.