Based on on the info you gave, I’m assuming your setting the default browser through
default apps >
Can you try going to
brave://settings/ and setting it to the default browser there.
Also, can you go to the settings within Outlook and setting the default browser there.
settings > apps & features > apps group > default apps. At the very bottom there should be a setting for your default Web Browser. (the path may not be exact)
And then quitting both apps, reopening and trying to open a link.