Section 3 of the 14th Amendment does not require any specific test which defines “insurrection”.

Ya, the real problem is that it doesn't. As specifically stated by the CRS:

Determining who has engaged in either of the two disqualifying activities—that is, engaging in insurrection or rebellion or giving aid or comfort to an enemy—is likely to be a difficult task given the scarcity of precedents and lack of clear definitions

And that difficulty is why that whole document exists, there isn't clear legal guidance. And the historic precedents on it are a mess. Yes, either house of Congress has the power to refuse to seat a member of their respective house and have used the 14th Amendment as a reason in the past. Moreover, Congress could pass a law which sets out a legal framework; but, that's not really happened either. The whole reason that this is even a discussion is that lack of clarity.

Republican strategy has long revolved around the targeted devolution of norms. They hide in the cracks between definitions which assume good faith participation in the labor of mutually consensual governance and shield themselves in perpetual faux-victimhood. If Congress does not pursue the execution of Section 3 it is nothing less than an abdication of their duty to their Oath of Office.

Arguably, Congress did try to do something, the House Impeached Trump. The Senate dropped the ball. And the American people then buried that ball far enough to interfere with Satan's daily activities by re-electiong Trump. It's a bad situation, but also not one we're going to solve by misrepresenting the law. Especially by handing The House the sole power to determine what Presidential Candidates have engaged in insurrection by a simple majority vote (the requirement to impeach). If you want to bring up "devolution of norms", that sort of power is going to take the cake. Anytime we have a split government, we're going to see impeachment and barring from office on the flimsiest of excuses. What we need isn't half-baked ideas but an actual, well considered framework.

Your last paragraph is a result of misunderstandings and assumptions on your part.

I think it's down to you moving the goalposts. You specifically stated:

The language of the 14th doesn’t require an impeachment or other formal conviction to apply. The fact that Trump was successfully impeached for inciting an insurrection is enough. The Senate’s failure to execute its duty does not erase reality.

You are arguing that the House Impeaching is enough to trigger Section 3 of the 14th Amendment. Which is what I'm calling ridiculous. Trump being convicted by the Senate would have clearly barred him from holding office again. The reality is that he was acquitted. That's the part which is actually important.