I have been using Pinboard (https://en.wikipedia.org/wiki/Pinboard_(website)), which is paid, though it's down today (the host is not even found in DNS), which is why I went looking for any posts on the general subject. On the privacy front, I have not investigated how secure their private bookmarks really are.

I have heard of Raindrop (https://raindrop.io/), which has free and paid versions. On the self-hosted side I have heard of Linkwarden (https://github.com/linkwarden/linkwarden).

But Pinboard is the only one I've used, since Delicious went under long ago.

[Note: This is my first PieFed comment, so I may be doing it wrong.]