It may not be exactly what you're looking for but BankStack would work with your current bag mod and allow you to sort your bag by item type (For example: Equipment goes to the top, vendor trash to the bottom.).
If you want a bag mod that separates items into their own category, then you might want to try ArkInventory. I have never used it personally, but after installing it to verify that it works, it seems you would have to set up the groups manually. But if you take the time to set it up, it should be exactly what you're looking for.
I'm sure there's probably more addons that might do what you're asking, but these are the two that I know of.
Arkinventory is what you want, I use it to sort everything. Quest items, Gear, Mining stuff, Cloth into thier own little sections of my bag and bank, Guild bank. You can modify items too to sort exactly where you want them. You also might want to try "Item Rack" to quickly change gear sets if you don't use it already.