... anything plugged into the water heater socket OR any of the charger (house) sockets caused a trip while the alternate circuit was powered off. I didn't do any resistance measurements because my meter needed a battery. Also the black test button on the breaker would turn off the square green indicator light but as soon as I released the button the light would come back on. I think there used to be a click noise when it trips and it should stay off until I reset the breaker -- but no click. I'm suspecting the main breaker at this point.

This is a standard DIN 35mm panel common in European house wiring. Shouldn't be too hard to find replacements online. Delivery might be slow but that's OK this time of year.

Should I check further before ordering a new breaker?