I'm also looking for "Google Photos but self-hosted" with the main feature being automatic object detection.
I just tried the Photoprism demo (https://demo.photoprism.app/browse), searched for "person", "grass", "wave", "head", "eye", "neon" and a bunch of other terms, nothing seemed to find any pictures although I took the concepts from existing photos I found.
Back button is also broken on the demo, which makes it seem like the most basic UX is not there yet in the application.
I'm pretty happy with Synology Photos on my NAS. It's got face detection, interprets the exif and gives you geo maps, has albums and sharing. Got it set up for my entire family.
It doesn’t back up photos. It exports them. Not the same. Take a slow motion video. The version on your NAS will be 30 FPS, slowed down in the middle. For a backup I expect it to be the 240 FPS version.