I tend to find workarounds. And, I have written a long one for you, but I am not posting it here.
Because, maybe, now, you should take a shortcut (instead of slogging thru my suggestion) and get the attention of @Mattches, who is a member of Brave Support.
My suspicion is, that some flag(s), or switch,(s) is(are) stuck. Possibly, Brave Browser just barely flubbed an update, but did not detect the failure or failed to properly close out (document) its progress (and again, did not catch itself). The flag(s) would be something like:
Your suggestions helped me think of something. I use a standard user for my day to day tasks, and then I thought let’s try checking for updates using my administrator user and when I switched to my administrator user I was able to check for updates. You can see the attached screenshot.
Let’s hope this help others who may face the same issue.
PS. Still the browser should let users update with their standard users as well. I hope the developers see to this.