> We don’t have a word as popular and overused as “coup” to describe the attempt to shut down the transfer of power

The more technical term for the kind of coup attempted (an extension of power beyond the legitimate term or scope by or on behalf of the current leader, is “auto-coup” or “self-coup”.)

> But this did involve the storming of a legislature in session in a obvious attempt to thwart the proceedings in a power grab

I mean, that's a coup attempt. There's no need to look for another term. It was an incompetent coup attempt, sure, but the term still applies.