If you want a gas discharge tube and not vacuum, you can even drop the coil on the inside: https://hackaday.io/project/194683-plasma-toroid-sky-guided-...

But most hollow-state devices run on either DC or pulses, so coupled inductors wouldn't work.

That depends. Often vacuum tubes are used with DC (that is a rectifier) in some form though, in which case you can't do this since induction depends on AC. I'm not sure what purpose the article had for a triode though, depending on their application this might work.

Interesting idea! Wouldn’t have to be particularly high voltage either.