feat(components): replace vaul drawer with base-ui drawer

[lunaxislu]

Summary

• Replaced the base registry drawer from a Vaul-based implementation to @base-ui/react.
• Aligned drawer behavior with the existing Base UI components (Dialog, AlertDialog) so dismiss handling follows the same model in mixed stacks.
• Updated @base-ui/react from 1.1.0 to 1.3.0.

Changes

• registry/bases/base/ui/drawer.tsx - Rewritten using the @base-ui/react/drawer API.
• registry/bases/base/ui/_registry.ts - Changed dependencies: ["vaul"] to ["@base-ui/react"].
• registry/bases/radix/ui/drawer.tsx - Kept the Radix drawer shell/classes under the cn-radix-drawer-* prefix.
• Theme CSS (6 styles) - Split drawer tokens into cn-radix-drawer-*, cn-base-ui-drawer-*, and cn-drawer-*.
• Examples (6 files) - Migrated the API from DrawerContent -> DrawerPopup, direction -> swipeDirection, and asChild -> render.
• Docs - Updated content/docs/components/base/drawer.mdx.
• Build output - Regenerated registry outputs via registry:build (styles/base-*/ui/drawer.tsx, public/r/).

Why

vaul and Base UI use different dismiss contracts, so mixed stacks can produce race conditions around Escape and outside-click behavior. The base registry already uses Base UI for Dialog and AlertDialog, so Drawer is being aligned to the same model.

API Migration

Vaul (before)	Base UI (after)
direction="bottom"	swipeDirection="down"
DrawerContent (includes portal + overlay)	DrawerPopup
asChild	render prop
data-vaul-drawer-direction	data-swipe-direction

Test Plan

• pnpm registry:build - passed
• pnpm typecheck - passed
• pnpm lint - passed
• pnpm dev - manually verified the drawer examples (demo, dialog, rtl, scrollable-content, sides)
• Verified that the Radix drawer still works through the Vaul-based registry path

Preview

• I also deployed a separate preview project to visually compare the Base UI drawer against the existing Vaul drawer:
  https://ui-forge-web.vercel.app/base-ui/drawer
• This page includes the demo, dialog, rtl, scrollable-content, and sides examples.
• I also added extra UI examples for other Base UI drawer capabilities.

Context

• This PR fixes [feat]: cmdk and vaul still use radix with the new base ui implementation #9191 (Base UI drawer migration)
• This PR relates to [feat]: Publish new components from Base UI #10170 (Broader Base UI component direction)

If this is not the direction the shadcn team wants, or if there are any additional details I should verify for this component, please leave a comment. I'm happy to adjust the scope or close the PR if needed.

[vercel]

@lunaxislu is attempting to deploy a commit to the shadcn-pro Team on Vercel.

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[lunaxislu]

Superseded by #10430. The new PR starts fresh from the latest main with only drawer-related changes, restructured commits, and a clearer ownership model.