Emulator

By "doesn't work", do you mean that nothing happens at all when you try to use it? Or is there some kind of error message?

Does this work in older versions of Dolphin? If so, which is the first broken version?

What do you mean by "Keys/"?

Yes, nothing happens.
"Keys/" is the basename/class of the variable in the configuration ini.
The behaviour changed between 10599 and 10760. I think, it might be related to PR #6321, I have SaveTextureCacheToState set to False, to speed things up. Or maybe PR #8279.

Ah, so this is a problem with hotkeys? Do the equivalents in the Emulation > Save State menu work?

Yes, it works through the GUI.
I think the issue is a conflict with modifiers that doesn't turn the hotkey as exclusive.

Keys/Load State Slot 2 = F2
Keys/Save State Slot 2 = LSHIFT&F2

When I Press LSHIFT + F2 on the keyboard Dolphin tries to Load State Slot 2. This wasn't happening before.

Keys/Load State Slot 2 = `F2`
Keys/Save State Slot 2 = LSHIFT&`F2`

Yes, happens that I was even subscribed to the PR.
Tested your syntax but didn't work for me either so I'll keep the workaround until the merge.