Did you download thru github? I hear this is a problem. I have Brave downloaded on a Windows PC thru Chris Titus Tech powershell and I cannot update either.
I used the brave.com/download webpage with the download button. Even downloaded the beta 1.24 version.
This, after I uninstalled Brave completely, and flushed any remains in the HDD and from the Registry on a Win7 Dell Vostro laptop. The update error message still shows.
On a Win10 Dell desktop I do get a successful “Brave is up to date” message.