The circuit is really a lot simpler than y'all are making it. Look at the attached pic. I eliminated all distractions but left the B+ rail and bias supply intact. Hopefully it will be clearer.
But this filament also seems to form another path to ground for the PT CT, with its resistance in parallel to the 560R.
Yes, that's true.
There's yet another ground reference, after the inductor, through the 20K resistor!
That 3K and 20K form a simple voltage divider to knock the screen voltage down to 325V. That's all it does. This type voltage divider is common in old hifi amps.
What happens to B+ voltages if the 12AT7 filament fails by: a) going open? b) shorting internally?
a) B+ will decrease slightly due to the increase in the negative supply.
b) B+ will increase by about 10V. The PT CT will now be connected directly to ground.
And what happens to the power tube grid bias voltage under such conditions?
Well, if the 12AT7 filament shorts, the bias voltage goes to zero. So? The output tubes are also cathode biased so they will not be damaged. If the 12AT7 filament opens the negative bias voltage will increase and the output tubes will produce less power. Either way the 12AT7 filament fails, you will lose the magnetic phono preamp.
A little background on this bias circuit... It was very common back in the days when 6L6s looked like coke bottles. You've seen the more modern trick of putting a zener in the CT to reduce B+. That trick works because the zener will have a certain voltage drop across it. That voltage will be negative in respect to the chassis ground. So now, instead of referencing the B+ to ground, you're referencing it to some negative voltage. The negative voltage will subtract from the B+.
Putting a resistor in the CT lead does the same thing that a zener does, except the negative voltage dropped across the resistor depends on the load current of the B+ rail. Higher load current means more negative voltage dropped by the resistor. Since this negative voltage is applied to the grids of the output tubes, you have a kind of AGC (automatic gain control) for the power tubes. If the tubes draw more current, the negative bias voltage increases and tends to cut back on the power tubes conduction. And vise versus.
Any of this make sense yet?