I've got a Synology NAS DS416play for several years now as a trusty backup/storage. But not using their Photo Galary feature. What I like about Synology is their long term support. They still offer software updates for this rather old model.
I'm still using Google Photos as main photo dumping ground as it has clients for iOS and macOS which automatically uploads all photos there and of course for the search and sharing feature. I'm even paying for the extra storage needed to host all the family pictures on a 2TB plan.
My concern having only the Synology would be that in case of fire/flood/zombies I'd loose all this stuff. Sure it's a 4 disk raid, but I'd have to make regular backups off-site. Which is pita and expensive as well. Synology does offer Backup to various cloud locations though. But overall I considered this more expensive than just paying for the Google Account.
I'm using the Mail service from Hetzner. I did host my own eMails for more than 10 years but eventually decided it's too much hassle.