## Problem
The `ui-patterns/CommandMenu` exposes internal components that have the
same names as the base shadcn components they wrap. This create
confusion about which one to use and forces us to expose the base ones
with the `_Shadcn_` suffix.
## Solution
Rename those internal components to have `CommandMenu` in their names to
make it clearer they are meant to be used with `CommandMenu`. We will
then rename the shadcn base ones to remove the suffix.
<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit
## Refactor
* Standardized Command Menu component naming across the design system
for improved consistency and clarity. Updated component names:
`CommandInput` → `CommandMenuInput`, `CommandList` → `CommandMenuList`,
`CommandItem` → `CommandMenuItem`, `CommandEmpty` → `CommandMenuEmpty`,
and `CommandGroup` → `CommandMenuGroup`. Updated public API exports,
internal subpath references, all examples within the registry, and
implementations across documentation, studio, and application
interfaces.
<!-- review_stack_entry_start -->
[](https://app.coderabbit.ai/change-stack/supabase/supabase/pull/45996)
<!-- review_stack_entry_end -->
<!-- end of auto-generated comment: release notes by coderabbit.ai -->
Replace docs command menu with Command Menu V2 from ui-patterns/CommandMenu.
This introduces the prepackaged folder for the shared Command Menu, which contains commands that are shared across the sites (for example, docs search, theme switcher).
Commands that are only applicable to a single site are now defined within that site's own app folder (put them wherever makes sense for your app folder organization, as long as you use the hooks within a global CommandProvider it will work...)
Tested navigating around, using search and AI on laptop and mobile.
