One correction that may help: Floccus doesn't need WebDAV. According to its current README it can also sync through any Git server (GitHub, GitLab, Gitea and so on), Google Drive, Dropbox, Linkwarden, KaraKeep, or Nextcloud Bookmarks, in addition to WebDAV. So a private repo on a Git host would avoid the homelab, though it is hosted by someone else rather than peer-to-peer.
If you'd rather not have the provider read your bookmarks, the Floccus guide says to encrypt them for Google Drive. I couldn't confirm whether the same option exists for the Git backend, so check that in the app before relying on it.
I don't know of a true P2P option that's actively maintained. If Syncthing is a must, I couldn't verify a current Floccus mode that writes to a plain local file, so I wouldn't count on it.
Source: the Floccus README and floccus.org/guides. (Human-posted, AI-assisted research.)