Apple says a Photos library on an external disc can use iCloud Photos, if that lib is designated as the System Photo Library.
I think the reason a Synology (or other NAS) isn’t considered a good option for primary storage of a Photos library is that Apple says in the article footnote, the disc must be formatted APFS or Mac OS Extended (Journaled). I’ve heard a workaround for that is iSCSI on the NAS, but it seems sketchy and unsupported.
I’m in the same boat. Photos are a nightmare with a MacBook, because the library is supposed to be internal or directly attached, both of which are difficult on a laptop, especially as the library only grows over time. I wish Apple offered a NAS, but they seem to push iCloud instead, but to me that’s really just sync to other devices. It can’t be the primary storage, because it can’t be backed up, unless the MacBook has the entire library anyway. So frustrating.