If you are using Brave then you already know Brave Browser gives priority to your privacy that's why it blocks most of the trackers of every website you visit,
also by design don't include a feature that can cause the risk of privacy,
that's why like Google chromes profile feature that sync data to your account is not available in Brave Browser,
But Devs of Brave Browser knew everyone know has a mobile device that they use most of the time,
they always want their important bookmarks simple accessible over desktop and mobile device,
So Brave Browser has a cool feature Brave Sync that syncs bookmark between your multiple brave browsers without impacting your privacy,
you can read on Braves GitHub repo about How Brave Sync works
Now Back to Your Question
How to Enable
For some reason, if you don't see Brave Sync option in Your Browsers Menu then probably Brave disabled that feature momently,
you can re-enable Brave Sync
- Search Brave sync and enable it
- Restart browser you should now see Brave Sync option in the browser
Setup Brave Sync
Menu icon > Brave Sync
- select 'Start a New Sync Chain' and save it
- Open Brave Sync on another browser where you want to sync bookmark
- This time Select 'I have a Sync Code'
- You can also Scan QR code generated while creating Sync Chain
Now Bookmarks should sync up between two browsers.
Some times even after setting this up perfectly Brave sync does not work as intended then you can backup your bookmark and redo the whole process,
you can visit Brave support forum for help too.
But if you want to sync bookmarks between two desktop browsers like Brave and Chrome, Brave and Firefox then you should read How to Sync Bookmarks across browsers.