Why do firearms "report"?

The two are, in fact, related.

The original Latin (re- + portāre, to carry;), as you note in your question, is at the root of this.

Sound is said to carry sometimes. As in:

There were a lot of families in the hotel, and they were noisy. The sound carried into the rooms very easily.

Thus, we're talking about, not the actual sound, but the act of it carrying over a distance. There's always some distance involved. As in:

They heard the report of a distant cannon.

A reporter is someone who carries the news (his or her report) from where the event occurred to where the public wishes to hear, read, or see it (at any gentlemanly distance).

The meaning of report as a "resounding noise, sound of an explosion" dates back to the 1580s.

Its prior meaning dates back to the late 1300s, and meant:

"an account brought by one person to another, rumor," from Old French report "pronouncement, judgment" (Modern French rapport), from reporter "to tell, relate" (see report (v.)).

It seems the report of a firearm came into being because if one only heard the sound of the firearm being shot, and did not see the firearm being shot, that the firearm was shot remains a rumor.

It wasn't until the 1660s that a report was a "formal statement of results of an investigation."

(Online Etymology Dictionary)