Just looked and yeah, not far off when you buy new. An old PC with a couple of hard drives can do the trick, but obviously it's more work to set up.

The used and refurb market is your friend.

For large capacity refurb enterprise-grade drives, I recommend serverpartdeals

I've had some good 16TB drives from there for a good few years and still kicking. They can be a little loud though. You can get 10TB drives for maybe €250.

A Synology 4-bay NAS can be bought second hand from eBay for about €200-€300. They aren't very powerful but might be fine for Immich and pretty easy to use. Many come with some hard drives you can pawn off or get started with using a RAID config that means if one or two die you are fine. If the drives are second hand (not pro refurb) though do not pay more than 30% of retail price because who knows how long they will last.

Photos don't take up that much space. Even 100 000 photos tends to take up less than 500GB. Video is much heavier, so if you're a videographer you may struggle without reencoding.