Brave is Chromium, so theoretically it is possible to sync the user profile, which includes bookmarks that are stored in a file there (or ignore everything but the bookmarks file to avoid other potential conflicts). The caveat is that the browser will likely not be able to refresh the file in real time, so the only way to make it work would be to always make 100% sure that you close the browser on one computer, let everything sync, and only then open it on the other side.