Improve Menu component performance (#3685)

This PR improves the performance of the `Menu` component.

Before this PR, the `Menu` component is built in a way where all the
state lives in the `Menu` itself. If state changes, everything
re-renders and re-computes the necessary derived state.

However, if you have a 1000 items, then every time the active item
changes, all 1000 items have to re-render.

To solve this, we can move the state outside of the `Menu` component,
and "subscribe" to state changes using the `useSlice` hook introduced in
#3684.

This will allow us to subscribe to a slice of the state, and only
re-render if the computed slice actually changes.

If the active item changes, only 3 things will happen:

1. The `MenuItems` will re-render and have an updated
`aria-activedescendant`
2. The `MenuItem` that _was_ active, will re-render and the `data-focus`
attribute wil be removed.
3. The `MenuItem` that is now active, will re-render and the
`data-focus` attribute wil be added.

Another improvement is that in order to make sure that your arrow keys
go to the correct item, we need to sort the DOM nodes and make sure that
we go to the correct item when using arrow up and down. This sorting was
happening every time a new `MenuItem` was registered.

Luckily, once an array is sorted, you don't have to do a lot, but you
still have to loop over `n` items which is not ideal.

This PR will now delay the sorting until all `MenuItem`s are registered.

On that note, we also batch the `RegisterItem` so we can perform a
single update instead of `n` updates. We use a microTask for the
batching (so if you only are registering a single item, you don't have
to wait compared to a `setTimeout` or a `requestAnimationFrame`).

## Test plan

1. All tests still pass
2. Tested this in the browser with a 1000 items. In the videos below the
only thing I'm doing is holding down the `ArrowDown` key.

Before:


https://github.com/user-attachments/assets/513b02c1-fc69-47f3-a97e-c56d44dd585a

After:


https://github.com/user-attachments/assets/266236a0-b64a-4322-9a54-ead7fb62191f

Author: RobinMalfait

packages/@headlessui-react/CHANGELOG.md

@@ -7,7 +7,9 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ## [Unreleased]
 
-- Nothing yet!
+### Fixed
+
+- Improve `Menu` component performance ([#3685](https://github.com/tailwindlabs/headlessui/pull/3685))
 
 ## [2.2.1] - 2025-04-04
 

packages/@headlessui-react/src/components/menu/menu-machine-glue.tsx

@@ -0,0 +1,17 @@
+import { createContext, useContext, useMemo } from 'react'
+import { MenuMachine } from './menu-machine'
+
+export const MenuContext = createContext<MenuMachine | null>(null)
+export function useMenuMachineContext(component: string) {
+  let context = useContext(MenuContext)
+  if (context === null) {
+    let err = new Error(`<${component} /> is missing a parent <Menu /> component.`)
+    if (Error.captureStackTrace) Error.captureStackTrace(err, useMenuMachine)
+    throw err
+  }
+  return context
+}
+
+export function useMenuMachine({ __demoMode = false } = {}) {
+  return useMemo(() => MenuMachine.new({ __demoMode }), [])
+}