Google photos is the best I've found. Your privacy feature seems to be a "nice to have", so I would use that. The UX and cross-device syncing is far better than anything else I've used.

To your bonus points: Google photos web UI is truly impressive even ignoring the awesome search capabilities. They wrote an article[0] on how they built it and since then I've been keeping an eye out to use similar techniques in different applications.

[0]: https://medium.com/google-design/google-photos-45b714dfbed1