“He wasn’t sworn in”
True.
But was he “elected”?
Amendment XXII is incredibly poorly drafted, it does not declare a twice-serving President “ineligible to the office” - easy language to include if that’s what they wanted to do.
It presupposes the existence of “presidential elections”, when there are no such things in the Constitution, and it’s unclear on whom or what the ban operates - for example, in the nonexistent November “election” can Barack Obama or Bill Clinton or George W Bush “run”? And if they “run”, what happens if they win?
The only voters recognized by the Constitution are the 535 Electors appointed by the State Legislatures (plus the three Congress awarded itself in 1960 when the States unwisely ratified Amendment XXIII). Does Amendment XXII regulate whom they can vote for? It doesn’t say so.
And once their votes arrive at the Special Joint Session for counting, does XXII regulate what the President of the Senate (who counts the votes) may and may not do?
Doesn’t matter. The Electrical College (ht Homer Simpson) elects presidents. The HORs certify it. Not erected (ht Chuckie Shumer) not certified so Trump was never president twice until swearing in January 2025.
Technically, there was no vote counting on Jan 6, there was only accepting and rejecting of state certificates.
The President of the Senate (Pence) who held the gavel did not have the authority to pause, delay, or suspend proceedings in the event an objection to one or more certificates was formally delivered. The Session was automatically paused while both the House and the Senate returned to their respective chambers to consider and decide the rejection of a certificate(s).
It appears that Pence, a leader of the R party at no time made an effort to urge the pursuit of that course of action, notwithstanding credible evidence of voting violations in one or more states.
If we’re going to get hung up on legalisms then, I can assure you, we’ll all hang together.