Tools can use an expansion, but we still can't differentiate between "bags" and "sand bags."
Yes, you can. Sand bags are a completely separate thing.
Large pots and barrels are considered the same option, but at least you can turn off wood to force only rock/clay pots (or vice versa).
You're confused. Large pots and barrels are actually separate. Maybe you're thinking of bags and boxes? If you want to store just bags (not coffers and chests), then you set the bags-and-boxes type, and the cloth materials.
I'm not saying stockpiles are perfect, though. Far from it.
There was a bug with bags in glass production, where they would put things like seed bags in your bag stockpile and ignore the "sand bag" restriction. I guess it was fixed at some point?
As for the other, I last saw the "Large pot/food storage" and overlooked the "barrel" designation last I was fiddling with settings. I still turned off wood/stone to force one to take only clay pots, but you can't simply toggle a stockpile to only take glazed earthenware (to save for brewing) instead of unglazed. You need separate kilns and careful link settings to manage it as a clumsy workaround.
Boxes/bags (lack of) distinction is also annoying, as you have to remember to turn off cloth/leather to prevent bags from entering the stockpile. I don't think any other leather/cloth items go in that stockpile, so its mostly an issue when you are trying to place chests and coffers.
If Toady adds one thing to the stocks menu, though, it would have to be a search function. I believe DFHack has one, but a search menu like you have with the embark screen and the manager would speed up managing stockpile links immensensly. Trying to control material types when hunting through stone menus and branching off your food stockpiles (booze plants to the stills, dye plants to the qern, plant fibers to the farmers WS, everything else to the kitchens, etc) takes up far more time than it should.