Thank you radhoo@ for all your help.
I eventually found the fault in the tube. It was a small wire connecting electrode to the metal body on one ends of the tube. It must have been broken duren transport by vibrations. Wire looks flimsy and a bit old, doesn’t even look like copper but rather like aluminium or zinc.
Anyway, radhoo wrote up nice tutorial how to troubleshoot issues with the tube using multimeter and osciloscope, and we found out that indeed tube is dead.
After replacing tube for new tested one (it is a little hard to solder it properly, but possible with lots of flux and solder and good solder iron), everything works perfectly.
It is also reading correctly (confirmed on second unit)!
Still the glass tube in the “broken” tube itself is intact, and metal casing too, so it should be easy to reuse it or fix with a piece of wire.
It might have helped a little to prevent this damage, if the tube was strapped to the pcb in the middle of its length. There are even holes to do that on PCB 🙂
Case closed.