Is this setup good for my usecase?

So I fell into the Frigate rabbithole and at this point I was thinking if I would be able to have a setup that serves my usecase equally but only works on Home Assistant. Let me know if the following can be done without Frigate and only with an RSTP Cam and Home Assistant (running inside proxmox).

I want a camera to face my apartment door from inside my apartment so that when a burglar enters my apartment, I will get a push notification on my phone (motion detection). I can watch a livestream of the camera feed on my phone and the recorded videofiles are being stored locally on the Home Assistant server.
The camera should be toggle-off-able so that I only get notifications when I activated it as I leave the apartment and dont have a cluttered server with videos of myself walking in front of the cam.

In case that setup would be not optimal in my usecase because there is preroll missing with information on it: Is there an option to have a cam record 24/7 (when I activated it and am out) and only flag files that have motion?

Just use Frigate. It can be setup to recognise faces. It can then send notifications when some who is not known enters you apartment. You can also set notifications from frigate to only be sent when you are not home. All this is very easy.