UI - Premium Stash Management Tools

I've read some of the threads of people complaining how difficult it is to manage the stash. Some suggestions are going too far on the farming side (selling items anywhere, ...).
But since GGG sell bundle of stash tabs, at least we should be able to manage that accordingly.

Context and assumptions:

I’ve heard of people with 77 premium stash tabs, maybe that was a joke but I’m sure that a lot of players have an impressive number of tabs. Sorting all those items and moving them from one tab to another require a lot of time. A computer would easily deal with some of the most tedious sorting tasks.

Main idea:

A bundle of stash sorting tools.
It brings a interface with the ability to search items with their type, name, rarity, mods, quality level, tab range, etc.
Search result is shown in a window that allow selection of multiple items in order to move them to one of the stash tab.

Related ideas:

A button to run a compacting algorithm to coalesce free space in one tab or a range of tabs.

The ability to define an area in the inventory, where items would be targeted for a drop-all or sell-all button. Obviously the items you always want to keep in your bag are outside this area.
Instead of using such an area, inventory items could be individually marked as non auto-selected for those *-all operations.

The tools bundle could be free but unlocked when you reach n tabs, extra tools above n+m tabs.