That was what I thought at first too. However if it were pressure change, the sound would change when you move the knob, not when the hot water reaches the shower.

Also it's more-or-less the same pressure. It's the cold supply pressure pushing water out of your tank or through your tankless water heater.

Yes, the thermostatic mixing valve is worth understanding- it’s pretty neat.

In most plumbing (at least in the US), there is no difference in pressure between hot and cold because the hot input is the same cold water source.