There is no ‘Brave Cloud’ from which your Bookmarks would be recovered.
Brave Support will likely need to know:
Your computer device type and its Operating System (“OS”)
Brave Browser version numbers
Do you have a Brave Sync chain set up? (If so, you might be able to recover your Bookmarks from a computing device that is part of that Sync chain.)
More questions
Is your Bookmarks collection aboard your Chrome browser installation, close enough - as a near-match - to the Bookmarks collection that you had aboard your Brave Browser installation? Could you get by, using a Bookmarks file that is exported from your Chrome browser?
Did you recently, manually back up your Bookmarks - using Brave Browser’s, Bookmarks Manager’s Export function? If you recently exported your Brave Browser Bookmarks on May 20, 2022, then the resulting HTML file will likely have filename: bookmarks_5_20_22.html
Did you recently, back up your BraveSoftware folder? Its location: