It's not CalDAV, but Joplin supports syncing with WebDAV and works great with Nextcloud (or any WebDAV server, really).
Nextcloud is a love it / hate it kind of thing. Since you're not already running it, I assume you don't want to (fwiw, it also does Cal- and CardDAV). Filerun used to be the go-to alternative, but it sold out and is all paid now. I'm not sure what took its place, but at the very least you should be able to setup a basic WebDAV server using just Apache.
The only thing I don't like about Joplin is it doesn't have a web app (at least, not as of the last time I checked).
There was another note-taking app I was thinking of and about to suggest, but it syncs over IMAP.