I’m actually surprised that the input gain of a preamp doesn’t really
effect the output signal gain of the amp. I thought it would be additive
or multiplicative (if that’s a word). Can someone explain why that is?
Is it that the output signal gain is usually the same (3-6db depending
on unbalanced / balanced) regardless of preamp?
The gain of the preamp does affect the output signal of the amp. But it does not affect how much gain the amp has. Different preamps have different gain and the same is true of amps. If you have a really efficient speaker, having a lot of gain can be problematic. But if your speaker is inefficient, that gain can be handy. Conversely not having a lot of gain is really handy with high efficiency speakers but won't work if the speakers are low efficiency.
So the equipment has to match. From a manufacturer's point of view, if the amplifier has about 25dB of voltage gain it will work on the widest range of loudspeakers. Amps with low power that are going to be driving more efficient speakers might only have 15dB of gain, and high power amps often have in excess of 30dB of gain.
The gain of the amp is different from how much power it makes. And the source signal can be different levels too. People often associate a certain position on the volume control with a certain amount of power, but really there is no correlation. Its just a level that works in a given situation.