We use Frigate with an Amcrest wifi camera. You need something relatively robust to run it on, although I think some people use a Raspberry Pi or similar. I went ahead and got a Google Coral device for the object detection.
This is pretty overkill for what you want, but Frigate is great. No need for an app, just use it through a browser.
Or are you looking for something to turn an old phone into a video camera?
Maybe a jitsi meet room with webcam would do. When doing it with a computer instead of a phone, you can set up OBS virtual camera (1 click thing) to add a filter that makes it grayscale, but that's slightly more clicks.
Regarding the warning for the fdroid app that was recommended by an other user, it might be ok if you place a clock with second-display in the view, so that you know if it has frozen.