I don't know about photoprism but I guess that's not going to work because it's really hard to provide features like face recognition and a web frontend with a zero trust setup. So if you just want the to have a automatic photo backup you could take a look at encrypted folders for nextcloud
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Last I looked Photoprism didn't support multiple users with different libraries at all, never mind encryption. There's an open ticket to support it. Immich has multi user support but not encryption.
I don't believe you're going to find a solution that has all the features of these and encrytion. The AI features such as object and face detection, as well as metadata extraction all run server side so the server needs access to the photo. Zero trust would require that everything runs on the client exclusively in which case the server is really just encrypted backup. I don't know of anything that works like that.
Nextcloud can be configured with end to end encryption but I don't know how other features work with that enabled.