Dylan definitely isn't properly using his vocal chords and body to do falsetto properly. Falsetto is a sound that's strictly in the ‘head’ and only uses the thin, leading edges of the vocal folds to vibrate, the chords technically don't even really "touch" the way they would if you were using your chest "voice" and breath from your diaphragm, that's why falsetto sounds so airy.
Compare that to head voice which is often classified the same thing as falsetto, it's more of a mix between head and chest voice and sounds far stronger as your chords actually "touch". Dylan is trying
way too hard to exaggerate the sound of a woman singing in a soprano range and it sounds like nails on a chalkboard. As a comparison, when a properly trained classical soprano sings, she uses her diaphragm for breath and power, and sings from the chest which means the vocal chords are, again, actually "touching". It's also why good opera singers are so goddamn loud, the power from your diaphragm is insane when you know how to use it to project your voice and properly execute vibrato. Head voice only really comes into play for a soprano when she is going super high up in the notes, and even then she still has that power to help reduce the strain on her vocal chords.
He's absolutely damaging his vocal chords doing this, which is a shame really as he has a decent voice when he's not being a degenerate troon.
Here's a classic example of an absolutely gorgeous soprano voice. Elaine Paige from Cats: The Musical before the movie ruined it. Skip to 0:45 for her to start singing.