1.16/20w06 update: It seems like the 1.15 version of the mod works as well, as long as you update the Fabric API (hint: https://www.curseforge.com/minecraft/mc-mods/fabric-api/files/2875599)
Version 1.4 (available for Minecraft 1.14 and 1.15) adds the sort icon to all inventory screens, and sorts items by display name / damage / enchants if the item type itself is the same. Also, the shortcut keys (sort chest, sort inventory, move stuff up/down) can be bound in Options/Controls now.
This mod adds some buttons around the standard chest GUI:
- move a whole row, or column, of items from your inventory to a chest or back
- move all items from your inventory to a chest that already occur in the chest
- sort your inventory, or a chest's contents
If you don't like the icons, there's a resource pack to change them (https://www.curseforge.com/minecraft/texture-packs/easierchests-alternative-icons).
Clicking one of the green arrows to the left, above, or below the original chest GUI will move all items in that row/colum from/to the chest.
Clicking the broom will sort the chest, or the inventory, next to it.
Clicking the right green arrow moves all items that are already have an instance in the target inventory. In the above example, I could shift-click one of the haystacks to move it, then click the down arrow to move all the other stacks as well.
Imagine you have 4 chests - one for cobblestone, one andesite, one diorite, one granite. You arrive home from mining, with a mixture of all of them in your inventory. Open diorite - click arrow - open andesite - click arrow - open granite - click arrow - open cobble - click arrow, and you'll have all your mining results sorted right where they belong.
You can excempt individual slots from sorting/moving by clicking the middle mouse button on them; these slots get marked with a red circle. Shift-clicking the broom or arrows overrides these exceptions.
This mod works with servers as well, as long as they don't explicitly disable some actions using NoCheatPlus or else. However, this mod doesn't allow to do anything you couldn't do without it, it just saves some clicks; so you might be able to talk to your server owner about it. No plugin is neccesary on the server.