Not sure if the following will help but it may. I’ve been running Brave on and off since 6 months ago and recently installed the Dev version and then the Beta version when it became available. A couple days ago we started having problems with the Beta version not wanting to update–fixed now. I went ahead and found that installing Brave now is the one that uses the Chromium look. After that, an app that I was using started opening the old version of Brave when I clicked on a link there–even though I had Brave set as my default browser.
I ran a search about the issue and someone suggested switching the default browser to Microsoft Edge (temporarily) and then back to Brave. Not sure if it worked for me that time or after I was careful to uninstall the original version of Brave–leaving both the Beta and the newest versions on the computer.
Anyway, try switching the default browser to Microsoft Edge (or something else) and then back to Brave. Hope this helps.