The beeping was your LPG detector, not the smoke detector. LP detectors emit a beep when the voltage is too low for them to operate - which is what I would expect with a dead battery.
First test is to disconnect the battery from the camper and put it on a charger overnight to make sure it is fully charged. Then let it sit - no charging or discharging - for at least 3 hours. Take a voltage measurement and it should be 12.7 volts. Then hook it back up to the camper and turn on all the lights. Assuming you have incandescent lights and not LEDs, that should be a good amperage draw. Take another measurement while the lights are on and the voltage reading shouldn't drop much. If the first measurement wasn't 12.7 and the 2nd one wasn't fairly close, the battery is damaged.
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