> "Servo Circuit" - hmmm, wondering if this means pulsing, as in controlling a servo motor.
There's a zillion different kinds of "servo", many don't pulse.
In audio, "servo" is often a very slow amplifier to set bias conditions.
> "....low voltage, low current supply to the heater elements in the tube. Since the tube is now running at such a reduced supply level, the anode current is much smaller than normal."
Conventional small tube heater-cathodes are set up to supply 5mA-20mA plate current. This toy is probably running below 0.05mA. It "can" be run with much lower cathode heat. (It would be even more efficient to use a smaller cathode, but choices are limited, especially for Production.)
However, working far-far below normal plate current AND at lower than normal cathode heat, the tube characteristics are not specified and not particularly predictable. If you set say 0.5V grid-cathode bias, one tube may flow 0.01mA and another may flow 0.08mA. OTOH, bias current is fairly critical because supply voltage is not a lot higher than signal voltage. We need to aim to the center of the range, not wild variation from one tube to the next or the same tube as battery runs down and the tube ages.
A fairly simple and super-cheap op-amp can compare plate voltage to half (or "whatever") of supply voltage, and push the cathode around so-that plate stands very close to design point. Like that, it would also null-out the signal, so a capacitor "slows" it so that correction takes seconds: slower than signal but faster than warm-up and tube/battery drift. This part is inoffensive. Historically absurdly expensive, but today just pennies.
Theory is one thing. "Tone" is something else altogether.
They have, of necessity, gone "cool". If you were to go the other way, an impossibly hot cathode with impossibly small grid spacings, you get devices very much like FET transistors and ultimately like BJT transistors. One of the rare W.E. microwave tubes borders on silicon performance, gets within striking distance of Shockley's Law which defines the maximum transconductance versus current of any field-control device. The Conventional Tube is an area on a whole continuum of devices. It seems to be a sweet-spot for audio "tone". I'm not sure how far away from "210V 1.5mA" we can go and still be "sweet".