No it doesnt. It leans that way on the official site but self hosters tend to use github or similar rather than official websites.
Source: Been self hosting it for months for free (I intend to donate to Linkwarden when I do my next round of self host/FOSS donations)
Save notes? Joplin has a configurable backup plugin built in. From memory you need to go to Options >Plugins & enable it.
Edit: I just saw you meant sync. Several ways with Joplin. Been syncing through Nextcloud with WebDAV which has worked great syncing between several devices ever since I started using Joplin. On Android you need to keep the screen on during initial sync which can take a while but after that sync is a couple of seconds.