You could get a dash cam and have it hardwired so it doesn't drain the car's battery when it's parked. You'll need one with intelligent parking mode so it switches off and saves power, only turning on when it detects motion, plus good night time recording so it'll hopefully record reg plates even in the dark.

I'd recommend the Nextbase 322GW, 422GW or 522GW. Or the Garmin 55. Alternatively, a trail camera (which are usually used to record discreet footage of wildlife) can be hidden inside, or outside the car, and pointed in the direction of the side it's usually keyed. The bonus of this is that it's cheaper than a dash cam and doesn't need to be plugged in overnight.