Tube amps consist of AC signals over high voltage DC . The coupling capacitors are there to block the high voltage DC and pass the AC signal from one stage to the next . If you get no signal through the coupling capacitor it's either no good , to small of a value , the tube is faulty or not connected correctly . So you won't be measuring any signal on the high DC voltage side of a coupling capacitors or the output transformer with an oscilloscope . It's completely unnecessary for one , not to mention dangerous . Especially if that DC voltage exceeds the maximum voltage rating of your oscilloscope . If you connect all your ground clips to the common ground of the Amplifier you can find all the information you need from the low side of all coupling capacitors alone . Even if your checking that the power filter is delivering clean DC without a differential probe you can see that clearly when your low voltage signal is clean without AC modulation from the supply . Or if your still unsure connect a 100nF capacitor to the end of you probe to block any high voltage DC . 100nF is plenty to pass all of the AC signal to your oscilloscope yet block the high voltage DC.
Even tone control will be low voltage because nobody wants to mess around with potentiometers with 100 to a 1000 Volts passing through it . If your design is correct you don't need to measure any high voltage with anything other than a multi-meter.
The only way to totally float your tube amp is to remove the earth ground entirely . But as soon as your connect the oscilloscope ground , the amp is no longer floating , so connecting the ground of your second probe anywhere other than where the first one is connected can be lethal because of the potential voltage difference . Regardless if you have a isolation transformer or not .
Amazingly, people worked on, & probed tube equipment with 'scope probes for decades, myself included.
We actually knew how tube equipment worked, & our work practices reflected this.
The reason why coupling capacitors are used is because the signal on a tube anode is indeed ac superimposed upon a DC level.
The next tube stage requires a fairly low negative voltage between grid & cathode to bias the tube into the correct operating state.
Unlike transistors, a tube with no bias voltage applied between those electrodes will be turned on, & conduct reasonably heavily.
If the grid to cathode voltage becomes positive, the tube will conduct
very heavily, probably to saturation.
Without coupling capacitors, tube stages would need to be hung "like beads on a necklace" across a very much higher HT voltage than is used in normal practice.
The ac signal is present at the anode of the previous amplifier stage, &
can be observed there with a normal Oscilloscope using a X10 probe, either on "ac coupled", or in many 'scopes using "DC coupling", because they are provided with a variable "DC offset" function.
With those 'scopes having very low voltage rated input caps there may be a problem on " ac coupled"
IF you are looking at the raw HT supply rail, but in an audio amp, all the stages before the output stage have anode load resistors which will limit the current available to damage the cap &/or input stage.
This is certainly not a problem with classic analog 'scopes!
Oh, by the way, in your original example, any damaging current through the ground clip will again, be limited by the anode load resistor.
i appreciate you may have limited experience with tube circuitry, & have bought "hook, line & sinker" into the "Ooo, scary!" narrative, but that is not a reason to try to refute information from those with that experience & theoretical knowledge..