Indeed a comment in OEIS A321676 points out that a 24 to follow 22 depends on not counting the Y in twenty-two as a vowel. It should be counted as a vowel (see below). When it is, the next number would be 25 rather than 24. I'd go further and say w is a vowel (in English), making the next value 27.

A letter's classification as vowel or consonant depends on its pronunciation when it's not silent (based on how much and how that vowel is sounded). The y in cry is pronounced the same as the i in ice. This is why some say that y is sometimes a vowel. The claim is that the y in yellow, say, is a consonant, but it has a long e sound; it may be a shorter period of time but it's the same formation. Compare the name Yago, which could be spelled Iago; it's just like the case with "yellow".

Now take W (please, to quote Henny Youngman); it's called (in English) a double-u, not a double-v. The English word West is pronounced the same as the French word Ouest. The same with Oui and We. Does anyone doubt the vowel nature of the Ou sound?

I hope that was enough trouble to sound off on for this puzzle. ... or should we go on to the later portions of the sequence to see what happens after the first number over 100? The list shows 103 followed by 109, rather than 110, showing it didn't include a count for the A in and. (Is that part of the specification of U.S. English?).