Like a shotgun blast, if you intend to do playalong recordings, you must pull the trigger on identification of what signature key the playalong is recorded in and play in the same key albeit doably transposed for the Bb trumpet or cornet. Otherwise, you'd murder the song and your recording.
I've bought lots of sheet music for musicals, that were not scored in the same key as they were performed / recorded ... not even in the same key as originally composed. What key music is performed / recorded in is usually the option of the producer, who may concede to the whims of conductor or lead performer. That's not to say I haven't listened to music played like it was in the key of H***, even some of my own playing.
I am as comfortable in the bass clef, as I am in the treble, still also playing a euphonium, and have played trombone, tuba and Sousaphone, and still doing a little baritone voice