Okay, so I was thinking about how Inventory ReInvented could become the best option for gamepad players, and I came up with this. The arrows indicate the movement path when pressing each button:

Red Arrow: D-Pad Down / D-Pad Up (moves the selector up and down in the item list)
Blue Arrow: D-Pad Right / D-Pad Left (moves the selector left or right in the item list)
Green Arrow: R1 / L1 (changes the container in the focused panel)
Yellow Arrow: R2 / L2 (switches between panels)

Image to visualize: https://imgur.com/AXnGq7f

Note: On top of that, I think the selector should "loop", for example, If the selector is on the last item of a column, pressing D-Pad Right will move it back to the first item of that column. Likewise, if the selector is on the last column and the player presses D-Pad Down, it will return to the first column (vice versa applies).

Image to visualize: https://imgur.com/zTcWGX5

Currently, Inventory ReInvented has the same level of efficiency as the vanilla inventory for gamepad users - you have to go through every item until reaching the very bottom or top. However, this layout I proposed makes the navigation more intuitive and improves the gameplay experience for those using a controller because it makes use of the way Inventory ReInvented organize items by columns of each category to create quicker ways to access stuff while also giving more defined button actions for better navigation.