The 13th ended slavery. You're probably thinking of the 12th which says that no person constitutionally ineligible to "be" president can be elected as vice president. Importantly, the 22nd only places limits on being "elected" as president, so it's not (necessarily) creating a constitutional requirement to "be" president by some other means.
Like I said, it could be an interesting legal fight if it even came up.
When I was 25, my girlfriend complained about buying the same bra, same size, same material, same URL, from the same company, on their website, 2 years apart. The first ones fit really well, the second ones didn't fit at all.
Meanwhile, there's a shoe that I buy a pair of every few years. They release a new "version" about once per year, but the fit has been consistent, so I'm over a decade, and 6 pairs, into my purchase of them, with no problems.