Change menus to fade out with a slight delay so settings changes are visible

[peppy]

Useful for cases like #31778, where a change to one setting can affect another.

osu.2025-02-03.at.08.36.58.mp4

[bdach]

Did / do you want this change to also apply to context menus? Asking because OsuContextMenu overrides AnimateClose() and does not call base:

osu/osu.Game/Graphics/UserInterface/OsuContextMenu.cs

Lines 60 to 68 in b60a834

	protected override void AnimateClose()
	{
	this.FadeOut(fade_duration, Easing.OutQuint);
	if (wasOpened)
	menuSamples.PlayCloseSample();
	wasOpened = false;
	}

so closes on context menus are still not delayed on this branch as it is.

[peppy]

Have applied this, good catch.

[Joehuu]

This somewhat resolves #12894, but I can still see the illusion of two checkmarks if I'm focusing hard enough. FWIW the OP video that had the 300ms fade out before improves that situation for me.

This also makes it possible to double-click a menu, but maybe not a problem?

[peppy]

I can still see the illusion of two checkmarks if I'm focusing hard enough

Potentially a monitor ghosting issue. Not really much can be done here, it's already an immediate hide.

This also makes it possible to double-click a menu, but maybe not a problem?

Doesn't really change that, just makes it more possible. I'll see what I can do.

[peppy]

I tried to fix the clicking-during-fade but it's not easy (the click handling is in the item itself which has no knowledge of the menu's state). Probably best left for another time.

I did end up doing a refactor to avoid the mind-boggling Animate method implementations. Pretty annoying change to review due to the flags involved, but I've checked that the sounds still sound correct to the best of my ability.

[bdach]

audibly the refactor commit seems correct.

i give it a ~20% chance that someone is going to complain about the delay but let's see if it actually happens