I have a raspi sitting idle and would love to use it to run this! What are common solutions for backups? I would hate to lose all my photos. Is buying a Synology the only option?

There's lots of other options... I'm not sure I could recommend Synology these days as they've started to vendor lock to only their drives, etc.

You could get a NAS from TerraMaster and swap the OS for TruNAS Scale or Unraid. They're relatively reasonable for the hardware, you can also DIY the hardware but that brings in other issues. Got an F4-424 Pro for a backup NAS myself. Worth noting a few big drives will cost you more than the other hardware though. 12TB was the pricing sweet spot when I got mine.

https://www.amazon.com/dp/B0CPPD51B9?th=1

In my case, all photos are stored in Synology, then run nightly backup to Backblaze.