Seeking advice on water heaters

[Jack the Greater]

31. And the pilot light needs the thermocouple to work to stay on when lighting

NBachers has it right. If the pilot burns while depressing the knob while lighting it, but goes out after releasing the knob (providing the knob was depressed long enough to heat the thermocouple sufficiently}, that is a very strong indication that the thermocouple either needs cleaning or replacing. Much less likely is the gas supply solenoid in the gas valve needs replacing, or replace the gas valve. But both are way cheaper than a new water heater, which is probably why RR did not mention it.

But start with replacing the thermocouple. That is what any competent honest service person would do.