Adding boarding pass from Messages to Apple Wallet fails

The last two times I flew with Southwest, I had them text me my boarding pass. In fact, what they text is a link. When I click on that link, it opens my default browser, Brave, and Brave gives me the following error:

Failed to Add Pass
An error occurred while adding the pass to Wallet. Please try again later.
Ok

Pasting the same link from the text into Safari adds the pass to my Apple Wallet just fine.

I’m using Brave 1.32.1 (21.10.28.15) on iOS 14.7.1.