If the transporter breaks a person down, converting them to energy, and then converts that same energy back into matter on the other end, maintaining continuity, the events of “Second Chances” could not have happened. At best, we would have ended up with two signals, each containing half of Riker’s energy. The only reasonable explanation is that the transporter cares little about what matter it uses to rebuild you. You are wholly deconstructed on one end and built anew on the other end, out of whatever is available. All that’s sent through is a blueprint. Continuity severed.
This entirely changes the way the citizens of the Federation interact with the transporter. The fact that you are scanned, deconstructed, and rebuilt almost immediately thereafter only creates the illusion of continuity. In reality, you are killed and then something exactly like you is born, elsewhere.
There’s a whole philosophical debate about whether this really matters. If the person constructed on the other end is identical to you, down to the atomic level, is there any measurable difference from it being actually you? Those are questions we can’t begin to answer. What seems clear — whatever the technical manual says — is you die when you enter a transporter, however briefly.