The pilot lights I’m familiar with just light the rest of the flame directly since they are burning already - turning on the fuel is all that is required. What systems uses a thermocouple and a solenoid?

Approximately all gas appliance pilot lights.

https://www.acservicetech.com/post/how-the-gas-pilot-light-f...

I've got a Honeywell digital controller on my hot water heater. It's powered by the thermocouple. It can make troubleshooting a lot easier because it has flashing lights for diagnostics.

It’s extremely common for the mechanism that only allows the fuel to be turned on if the pilot is lit to work by having a thermocouple in the pilot flame. Some of these also power the controls (thermostat, for example) and some don’t.