There is currently no way to change that.  Syncing all the browsers immediately when any change is detected in any browser minimizes the possibility of syncing conflicts.  And to sync with Brave requires using our extension which requires that Brave be running.  Back in the old days, we had reverse-engineered browsers' bookmarks files and could make changes while browsers weren't looking.  But nowadays, the Chromium-based browsers can check to see if any changes were made behind their back like that, and they sometimes barf.

An alternative design would be for our agent could hold on to changes until Brave was launched.  But then if the user had made changes in Brave on a different device, and both the changes from Brave on the other device and from other browser(s) on the current device would hit at the same time, making a possible sync conflict.

To avoid the annoyance of Brave launching and taking over your screen momentarily, we recommend leaving Brave running at all times (by making it a Login Item), keep one Brave browser open, and keep that window minimized to the Dock.  This way syncing can occur silently and invisibly.

(The requirement to have a browser window open in Brave is due to a current bug in the Chromium source code which it seems will not be fixed for a long time if ever.)