New to me cub...no start

[Waif]

Your vid , you're getting off the starter before it could turn if engaged.
Sounds like it's popping forward like it should.
IF it is not getting meshed with the flywheel teeth or the starter spring is weak it might not be meshing.
Turn the flywheel a little, which will answer your question of if it's stuck. Also will present different teeth for the starter to engage. Then try the starter again.
It looks like a replacement starter from the original. Unless you polished it up , it's not very old.
Any more trouble and I'd pull the starter and look for what is out of spec somewhere. Including checking the spring as well as it's attending functions in it's travels.

Clean up the casting where the starter bolts to it while it's off. Giving it a clean ground there.
Bolt holes holding it on allow a bit of play of the starter housing before tightening.
If something is a couple mills off... you have that wee adjustment available if you're mindful. So study the flywheel teeth for how they been getting hit if it's noticeable. Too little towards center of wheel , or too much.