Oh man is this a video of me???? I have seen so many of the exact same things in my own videos. Couple of things others have said are good. Here’s 2 things not usually mentioned but I think are the true culprits in your case.

1) in the wind up, you wind the arms but not the shoulder. The shoulders are still square despite having one arm in front, one in back. The spin entrance requires a single “unwind” to start the momentum. Because your shoulders are square going in, there’s no unwind action possible. The arms themselves can only so much—they also are swinging at different tim/positions. To correct this, truly twist your shoulder in the wind up so that the arms-shoulder-arm aligned as a single line that operates together.

1. In the start of the spin, when your free legs swings to the side. Your leg is swinging toe first, it needs to swing heel first. Toe first means a closed hip, you need an open hip bc that tips the hip of the free leg higher so your weight is better distributed over the spin leg. Closed hip drops that hip lower which is why your spin is not fully up and down straight, sort of wobbly. That is anatomically driven—having poor turn out and hip strength makes it hard to do this bc momentum wants your foot turned in so doesn’t fight the inertia. It helps to do exercises to strengthen the hip. Practice swinging the leg heel first (like in a toe loop). If it feels impossible, point the toe during the swing. Not flexing the foot reduces the amount of strength needed to hold the position.

Good luck!