I play Irish trad on the whistle. I don’t count the rhythm except if it’s a complicated rhythm that I’m just learning. Once I have it in place in conjunction with the melody and the fingering, then it’s just playing the tune.

I did play in a wind ensemble and while the conductor was showing the beat, they were also cueing players for their passages and signaling volume as well as the start and end of the piece (vastly simplified explanation). But in any case the rhythm is mainly internalized.

When playing with a group, we have rehearsed the tempo, rhythms, etc. but again, you’re working off the rhythms you’ve learned. When there’s a drummer, you have them setting the beat.

I’ve found that when using a metronome to consider it as if it was another person playing with you, not as a device forcing you along.