What in the actual fuuuuuuudge is goin on here?

Special stash tabs like gems etc can be associated with for example gems then you can just open stash and shift click and it Will aoutomaticly go to the right tab

Yep as Ort sais
You can do this with:
Essenses
Delerium & Delerium maps
Currencies
Skill, Support, Spirit gems
Flasks
Uniques (up to 1 per unique type)
With the special tabs,

You could also do this with normal premium stash tabs if you tag one one of those affinities, then these items will automatically go into that tab

Yes but I mean you can't auto sort your inventory or your tab like how d4 implemented. I just think that is a super helpful feature and saves alot of time

As far I am aware macro's for NON GAMEPLAY related things are allowed ... questionmark? ...
Not sure if I did read that correctly, so perhaps check their rules first and maybe that can get you further?