I think if your photos are on any kind of public website, AI idiots will scrape them regardless of the provider. So at minimum you have to password protect them. That said, I’d feel ok using this:
https://www.hetzner.com/storage/storage-share/
It basically runs NextCloud. You’d configure it so that only logged-in users can view the pictures, and give accounts to your friends and family. I don’t think Hetzner is likely to train AI with it, though you could check through their privacy policy. Part of the issue with eg. Google Drive is that everyone wants stuff for free, so Google recovers some of its costs by advertising, AI training, etc. Hetzner charges enough to actually make a profit, while still being IMHO affordable at the level we’re discussing. That means they don’t have to do crap with advertising etc. I have 5TB in their Storage Box product and am happy with it.
If you want to be more hardcore, you could set up a dedicated server with an encrypted HDD, but now you have to deal with the hassles of self hosting, including backups. It still wouldn’t be end to end encryption, which would require your users to run some kind of special client, or maybe use some awful javascript client.
As always, Ada gets no respect.