Mine is plug in. If I lose power the gas furnace won’t run either.
Ours plug in, with a 9v battery back up.
Some have perished when the power goes out and they fire up an old wood-burner that they haven’t used nor inspected/cleaned for years.....
If the furnace has a pilot light then get a battery powered monitor. Pilot lights usually still burn power or no. If you have a gas hot water heater, oven, or dyrer same thing same risk. Any gas or fuel oil operated appliance or unit warrants a battery powered detector. It's money well spent.