

The wording is specifically that you need to be qualified to hold the office of the president, not to run for the office.
But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States.
With qualifications to hold the office being:
No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.
So the phrasing of the 22nd created an issue:
No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once
Elsewhere it talks about eligibility to hold office, but the 22nd only refers to election.
There’s also a similar issue with the speaker of the house, where eligibility isn’t as clearly defined as one might expect.
While the intent of the law was clearly to codify the previous pattern of capping it at two terms (and being spiteful to FDR) it’s phrased with enough ambiguity that it’s clear how they’ll argue it.
Right now there are three “biggest powers” on the world stage. US, China and Russia. China has belligerent rhetoric towards a lot of their neighbors, particularly Taiwan. They want the areas they control, but largely stop short of action. It’s why they claim the South China sea, and other nations need to pointedly ignore their claims to delegitimize them.
Russia has been openly annexing, or trying to anyway, their neighbors, and using historical precedent as their excuse.
As the largest power, the US very notably not annexing land nearby shifts the tone way into the realm of it being the norm not to do that.
Annexing, or at least threatening to, nearby land makes it more that all major powers do so, or at least are looking for opportunities to do so.
If cold war schemes give the US historical claim to Greenland, then Russias claims on Ukraine start being less unhinged and more generally expansionist.