This really isn't as complicated as you are trying to make it. There is no need to separate the touch and the catch. He popped it up, it was caught, period.
If he popped it up and F2 attempted to catch the ball, standing 3' in foul territory but bobbled it and the ball fell to the ground in fair territory...we have a touch in or over foul territory and thus a dead ball, foul (then we talk about the count, etc) - and the batter is out because his bunt attempt on the 3rd strike was bunted foul.
Your situation is just a catch, that's all. Forget the 3rd strike, forget the bunt attempt. He popped up to F2 - he's out because F2 CAUGHT THE BALL.
You won't have a coach try to argue the difference in touch and catch in this situation. It's a caught fly ball, the ball is live by definition.
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