For the advanced search functionality, yes you need to go to Linkwarden. Otherwise if you want the bookmarks to show up in the browser you can use a tool like Floccus.
In simple terms, link rot is when the contents of a link you saved from the past is longer available.
Firefox sync does save the link url itself, but the actual content is susceptible to being taken down for any reason.
A tool like Linkwarden both saves the link url as well as the content itself, so you'll have a copy even if the original content is lost. All while taking collaboration into account.
Linkwarden maintainer here, thanks for the shoutout and stay tuned for exciting updates as we have lots of new features lined up for the next release :)
Thanks, lmk how it goes!