How do I get YouTube links to open in the YouTube app by default?

I have an iPhone 13 mini running 15.6.1 with all apps updated to their most recent versions (as of 6/10/2023). When I tap a YouTube link, it opens in a new tab in Brave, my default iOS web browser. At the top right corner of the page, I can tap a button that says "Open App". When I do this, I get a popup saying "Switch to the app for a better viewing experience". When I tap "Open the app" I get another popup asking to switch to the YouTube app immediately followed by another asking to open the App Store.

So to open a YouTube link I receive from, for example, a text, I tap the link, tap "Open App" in the browser, tap "Open the app" in the first popup, tap "Don't Allow" in the third popup (the App Store), and then finally tap "Allow" in the second popup (YouTube app). Instead of a single tap as it should be, I need five taps and have a browser tab to close when all is said and done. It's almost like my device does not even recognize that I have the YouTube app downloaded. How do I make this happen by default?