Not sure how detailed you need me to be about "exact setup"...
This is an issue whether running on my Macbook Pro or my Mac Studio.
As mentioned, if I wish to start an application, my typical workflow is to activate Spotlight search with Cmd+Space and then start typing some part of the application name that I wish to start. If any Mail application window, Inbox or Compose window, were active when I activate the Spotlight search input, the keys which I am capturing with BTT in Mail to simulate Gmail key bindings are captured and unavailable to me in the Spotlight input. In order to have all keys available to Spotlight input, I must click a window other than Mail and then go back to typing in the Spotlight input, which kind of defeats the purpose of an all keyboard interface to starting apps.
Let me know if there are other specific details that you need.
BTW, this is the other post I found raising these same issues...