I know there's a way to hide/move the ones that are related to how it is sorted (the one with the label to sort by Name, Mod, etc. and the one close to it), but I haven't found a single clue on how to hide the ones closer to the player's inventory.
I was wondering if there was a way for me to hide/move also those buttons as I find myself quite comfortable with using shortcuts for sorting or alternative ways of inventory management (such as Inventory Profiles Next) and the buttons overlap (yes, I know IPN has a way to move its buttons but that doesn't seem to get it properly working due to its position being absolute and missplaced in higher tier storages).

So if I understand this correctly you want to hide these because you want to use IPN here, correct? I definitely don't recommend that because there are cases where IPN would need explicit compatibility with sophisticated to not cause item loss or dupes. And because of that I am also not in favor of adding functionality to hide these, maybe I will consider adding functionality to move in case there's some mod that adds something that's not sorting/transferring/searching and overlaps with these buttons.

That's fair too.
I may also go and just blacklist IPN from those screens, as it tends to bug quite a bit with its display on cartain containers (in fact, I've also migrated to using InvTweks Refoxed + InvEssentials in ATM10 due to it lagging quite a bit on sorting certain containers).

ok, I am closing this given that it's still better to use sophisticated buttons for this functionality rather than other mods.