It isn't "the narrative". The Honduran Supreme Court issues the arrest warrant. There was a congressional investigation that reviewed state department cables and found exactly what the part post is claiming.
“Narrative” would be when you use “U.S.-backed coup” to describe a president refusing to leave office legally and the U.S. working to keep him out. There’s valid criticism that the U.S. should have been more aggressive in condemning it as a coup but none of the evidence suggests that the U.S. supported a coup in violation of Honduran law. The State department cables which were leaked show their focus was on preserving aid to people until a new election.
No, he was term-limited to the single term allowed by the constitution and was running anyway, with a fig-leaf of a referendum for a proposed constitutional convention to retroactively legalize the second term, the timing of which could never have allowed him to legally run for president. This was a “constitutional coup” by the judiciary designed to prevent an illegal second term that was clearly otherwise going to happen.
The US government refuses to follow its own laws.