If messing with the Mains side of equipment power supplies is the most dangerous thing you do, you will live a long uneventful life.
Every time you become a road user of any kind, you are subject to a much greater accident risk.
Even something like cleaning your gutters is more dangerous, to say nothing of using any kind of power tool.
Tube/valve equipment , certainly, in Oz, normally had a power supply consisting of a transformer, the secondary of which, provided heater voltage, &, most importantly, a high ac voltage which was then rectified to give the tube's required dc HT voltage.
These secondaries were normally used with a two diode full wave rectifier, requiring a centre tapped secondary which provided, commonly, "285 volts a side", or for older equipment, "385 volts a side" for radios, & around "350 volts a side" for earlier TVs.
Obviously, the complete secondary would be twice that, giving 570volts, 770volts, & 700volts respectively for the above examples.
And they weren't little "pipsqueak" transformers, either, ----many were around the size of many isolation transformers.
There were also quite unpleasant dc voltages available.
People worked on this stuff with perfect peace of mind, as they knew " where not to stick their fingers".
Beginners commonly made Mains operated stuff without mishap, as they learnt "first up" that they were working with equipment which contained nasty voltages.
The traditional "ac/dc" design, such as the "All American Five", were hated, & dubbed "death radios" by Australian EEs & Techs, as they really do have the chassis connected to one side of the Mains .
Active or Neutral,? How lucky do you feel?

Modern equipment with SMPS is a totally different thing.
The "guts" that performs the desired function is isolated from the Mains, just as with a transformer/rectifier linear supply.
Unless there is a SMPS fault you should not be involved with any circuitry which has its "common" rail connected to the Mains., so can use your 'scope normally.
I used an isolation transformer extensively when repairing the power supplies of Television Picture Monitors & Receivers, but if there was no power supply fault they were unnecessary.
If you are going to get yourself so tangled up that you somehow zap yourself using an isolation transformer, I suggest you need to take a break.
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