Quite a few things going on here. Did you notice that the piece broke right off almost in the middle as you were splitting it? At that point the billet was eliminated from possible handle status. There were knots in the piece at both top and bottom. One of the knots is part of why and where your handle split when you tried to chisel in the wedge.
You want clear wood with as straight a grain as possible for making axe handles. That's one thing. You want to saw the kerf for your wedges. Driving a chisel into end grain is a splitting technique, you will split your handle doing that. Your wedge wants to push the handle against the sides of the axe eye, not the ends, so make your cut for your wedge in line with the axe edge, not perpendicular to it. You get much more are for pressure and friction pushing the sides out rather than the front and back. Use hardwood wedges the length of your axe eye front to back and make them three quarters the depth of the axe eye. Cut the kerf just a little deeper than the wedge is long.
An axe handle is a complete thing, not just the part that goes into the axe's eye. Make a handle that fits your hands and flows from the pommel swell up to the neck just below where the head sits, then tapers smoothly into the axe eye. Without the axe head in place, the handle should be a flowing continuum from top to bottom. It's not just appearance, it's functionality and strength. That sharp angular shoulder you made, where you put a tenon on your piece of wood and fit it in the axe? That's a good technique in wood to wood mortice and tenon joinery. But in hanging an axe, it creates stress points where things will fail.
Here's a link to someone who, if you can be patient with his presentation, can teach you a tremendous amount about how to fit an axe to a handle.
The other thing that was very apparent in watching your video is that all of your tools are seriously in need of proper sharpening. Not intending to be insulting, trying to help you improve your work and avoid injuring yourself. The kind of force you were using with that huge drawknife (I've never seen one with a blade that deep before) is difficult to control and that becomes dangerous. A drawknife should be razor sharp, able to easily shave paper thin curls off of a piece of wood. Same for chisels. Sharp is safe, dull is dangerous. Again, control is the key to safety, and sharp tools are much easier to control, because you can do the task with much less force.