I tried photoprism and thought it was pretty neat feature-wise. If I recall correctly they even sort received photos in a sensible date-based structure automatically. Don’t think they have an official app but maybe some third party stuff; the web UI is mobile friendly though.

To talk backups, I’d deploy the thing using containers and then back up the volumes any way you like.

This may not be the ideal solution for you, especially due to lack of decent android support. The workflow would probably be something like take photo -> sync to protoprism to sort -> view in photoprism gallery, which may also be too convoluted for you. Also, I’m not sure what you mean by the last paragraph.