I’ve rarely experienced Brave failing to update. “Rarely” is more frequently than “never”, but … rarely.
A few suggestions before doing anything desperate:
First, have you actually shut Brave down (“Exit”, not just minimize the window) before you attempt to update?
Next, have you rebooted Windows recently? Rebooting cleans the drains, so to speak.
What’s also worked for me if starting Brave and clicking “About Brave” fails to automatically / properly update when a newer version is available: download (optionally save) and use the appropriate installer from Brave’s home page https://brave.com/download/ Specific to this suggestion, when I’ve done this, the Brave installer recognized my existing Brave files and utilized my preferences — bookmarks, extensions, etc. — but I won’t guarantee that’ll be your experience.