Excellent bit of semantics at the start!

I just love your presentations style

Definitely on board with "Axe Grappling" and would even go so far as sharing the feature with the Sickle. In the Club video, I suggested calling this mechanic the "Hooked" property on the Sai while in the Shortsword video, I suggested allowing light weapons to attack as a reaction to Contested Actions, so same rules apply hear. Minor correction though: there is very little historical evidence for Vikings using the beard of the axe. They very much might have, but for all intents and purposes, we have no idea how axes were actually used over 1,000 years ago. Most of our evidence for axe hooking comes from late Medieval/Renaissance sources associated with the pollaxe and halberd, after one-handed battle axes had been rendered mostly obsolete by the widespread popularity of swords along with the ubiquity of metallic armor.

Just discovered your channel. Really good stuff. Regarding the Handaxe, and weapons as a system in 5e more generally, I believe there is a real opportunity to help address some of the martial/caster disparity by taking a longer look at weapons like you have here (and like Pathfinder does)

Going off previous vids, I granted it access to Tunnel Fighter as well, with the logic that a short hacking movement could technically be done with a smaller axe. With that said, probably a bit questionable on that part, and I do like the idea of the beard disarm as well!

The handaxe is already good in grapples because it's light...