Brave cuts into a tab, uninvited, when I swipe on the mac

I was working with ChatGPT. Many times when I use a gesture to switch between my desktop and the tab in Brave where I have the ChatGPT session, Brave cuts in inviting me to some Brave interaction I am not interested in. But I cannot go back to my ChatGPT session without losing the thread there.
I do not know what gesture it is, but it is definitely Brave, and it is definitely a legit Brave behaviour - but I do not want it and have no idea how to stop it.

Screeenshot? what exactly is it showing?

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