The general rule in the Class-A solid state world is to not exceed 30% of the transformer's VA rating for long term viability of the transformer.
In your example, a 100W per channel stereo class A amp could have a maximum efficiency of 50%, so your bare bones minimum transformer rating would be 400VA, but such an amp will also have multiple stages that also consume power and won't be 50% efficient, so you'd move up to the next size which is 500VA or 600VA. Which I would select between those two would depend on the amp design and the transformer manufacturer.
Sizing transformers for a tube amp is not nearly that simple, as there are tons of windings.
Some examples of tube amp transformers:
Dynaco ST-70 is about 300VA for a 75W amplifier.
Kaiju 300 is about 265VA for a 16W amplifier.
Paramour 2A3 was about 55VA for a 3.5W amplifier.
As you can see, these are all way, way, way above 3x output power.