How do I unBLOCK my camera for a telehealth session?

Sure. To shut down the iPad, Turn iPad on or off - Apple Support. That also addresses how to force it to shut down if it "locks up" or becomes completely unresponsive (which ought to be a rare event).

To wake it, Wake and unlock iPad - Apple Support

Sleeping the iPad is best accomplished by just ignoring it (that's what I do) but you can manually put it to sleep by momentarily pressing its "top button" — Use the Home, side, and other buttons on your iPad - Apple Support.

After a while all this becomes second nature.

I checked the doxy.me website help, and it explains everything better than I was about to:

https://help.doxy.me/en/articles/836274-camera-and-microphone-permission-safari

As such things go it's surprisingly well-written, but if something about it doesn't make sense please write back.

Maybe this is just your basic stop it “when in doubt reboot” thing? I never shut my computer down. I just put it to sleep at night.

Sure. That's what I do, since it's never necessary to routinely shut down a Mac. However, a simple reboot is justified whenever you suspect something isn't working properly.

Follow that doxy.me "help" page, where at the bottom it offers to interactively check your settings:

"You can also test permissions here to ensure everything is working correctly."

Everything worked as expected on an iPhone, an iPad, and the Mac I happen to be using at the moment. It all seems pretty well thought-out, so it stands to reason that their "please contact our support team" link ought to work too.

Other than that all I would suggest are the normal things to check when a website isn't working properly: no VPN, no "anti-virus" nonsense, etc, but if their support team can't help by all means write back. I'm not out of ideas yet.