Sorry to be cryptic; crazzzy day at work.
> rectified signal which comes back to the ef83 to control vr?
You got it.
The tube is specified to give varying gain without large distortion.
Of course we could run a steady DC voltage to it, to control the gain. Or trim a DC voltage with a potentiometer to control the gain. But it is (used to be) so much simpler/cheaper and cleaner to just run the audio through a pot to change gain. (Later came audio chips for TV sets that changed gain with a DC voltage, but that's a lot easier/cheaper to do.)
So the usual reason we would bother with a voltage-controlled variable-gain tube is so a lightning-fast electric signal (rectified from the output) can change gain and reduce peaks faster than the human hand.
Another odd thing about the schematic you traced: It seems that the control voltage is fed to the cathode through a low-resistance voltage divider. It is more common to feed control voltage to the grid, a very high impedance point. Driving the low-R cathode means LOTS of rectifier power which means a power amplifier. If I read that right, to get 16dB gain reduction, you need about 20V at the cathode, almost 20mA of current in the resistors, maybe 40V at the top of the divider, 40V*20mA= almost 1 Watt of power. If that is fed rectified audio directly, distortion is gross; you need a fast-attack slow-decay filter. That means the rectifier has to take enough power in the short attack to hold-up all through the decay. So the peak power needed from the amplifier is 10 or 100 Watts!
So there has to be something more.
You do not show any grid resistor on pin 9 of the EF83. There has to be one. The sheet says it could be as large as 3 Meg. Maybe that is where the control voltage is applied? Then your "feedback from ECC82" is probably just a DC bias voltage: they wanted to jack-up the EF83 cathode so it did not gain-reduce on small signals, and that ECC82 might just be a convenient source of a low clean DC voltage.
I am ordering a TK19 schematic from a small German shop. It may take weeks to pay, scan, ship, etc, but I like German service manuals from the 1950s and 1960s.