There’s a lot to address here as you’re talking about hardware and possibly multiple levels of software.
Yes, you can do this with raspberry pi or any SBC or mini PC. Even an old desktop PC if space isn’t an issue.
In terms of photo management software, I really like Photoprism. Immich seems to be popular as well.
In order to get your photos synced to multiple computers over the internet (a good idea for resilience), you could look at syncthing. Alternatively, you could have one central server and one or two backups in different locations using borg backup or similar. In my experience, backups are easier to manage and make it easier to recover from data loss than replicating the current state of your data in multiple places. You can do both, though.
It’s a very worthwhile project, but may be pretty difficult unless you are already comfortable with server technology or are enthusiastic about learning.
I watched the first season, partly because some reviewers pointed out that it depicted the multiple relationships of the protagonist more like an actual polyamorous relationship than a typical harem anime. I would have to agree with this specifically in regard to the first half of the season when there are two or three girls involved with the protagonist. He actually goes out of his way to understand the needs of each partner and diffuse conflicts between the girls.
However, this dynamic breaks down fast when more girls are introduced, and the show rapidly devolves into a typical harem comedy, losing any aspect of realism or wholesomeness. Because of that I have no interest in the second season as I expect it to only get worse.