Requires #16763 and #16753.

Moves all elements and templates defined in the `@payloadcms/next`
package to `@payloadcms/ui`. This is in effort to convert the
`@payloadcms/next` package into a framework adapter.

**Relocated exports** — code physically moved from `@payloadcms/next` to
`@payloadcms/ui`:

| Component | Old source | New source |
| -------------------------- | ----------------------------- |
---------------------- |
| `DefaultTemplate` | `@payloadcms/next/templates` |
`@payloadcms/ui/rsc` |
| `DefaultTemplateProps` | `@payloadcms/next/templates` |
`@payloadcms/ui/rsc` |
| `MinimalTemplate` | `@payloadcms/next/templates` |
`@payloadcms/ui/rsc` |
| `MinimalTemplateProps` | `@payloadcms/next/templates` |
`@payloadcms/ui/rsc` |
| `DocumentHeader` | `@payloadcms/next/rsc` | `@payloadcms/ui/rsc` |
| `DefaultNav` | `@payloadcms/next/rsc` | `@payloadcms/ui/rsc` |
| `Logo` | `@payloadcms/next/rsc` | `@payloadcms/ui/rsc` |
| `HierarchyTypeFieldServer` | `@payloadcms/next/rsc` |
`@payloadcms/ui/rsc` |
| `DefaultNavClient` | `@payloadcms/next/client` | `@payloadcms/ui` |
| `HierarchyTypeField` | `@payloadcms/next/client` | `@payloadcms/ui` |
| `NavSidebarToggle` | `@payloadcms/next/client` | `@payloadcms/ui` |
| `NavWrapper` | `@payloadcms/next/client` | `@payloadcms/ui` |

This PR also removes the now unneeded export aliases. These were in
place for backwards compatibility during v3. Now, we enforce that all
imports point to its canonical source, not the aliased export.

| Component | Old source | New source |
| -------------------------- | ------------------------- |
--------------------- |
| `CollectionCards` | `@payloadcms/next/rsc` | `@payloadcms/ui/rsc` |
| `SlugField` | `@payloadcms/next/client` | `@payloadcms/ui` |
| `QueryPresetsAccessCell` | `@payloadcms/next/client` |
`@payloadcms/ui` |
| `QueryPresetsColumnField` | `@payloadcms/next/client` |
`@payloadcms/ui` |
| `QueryPresetsColumnsCell` | `@payloadcms/next/client` |
`@payloadcms/ui` |
| `QueryPresetsGroupByCell` | `@payloadcms/next/client` |
`@payloadcms/ui` |
| `QueryPresetsGroupByField` | `@payloadcms/next/client` |
`@payloadcms/ui` |
| `QueryPresetsWhereCell` | `@payloadcms/next/client` | `@payloadcms/ui`
|
| `QueryPresetsWhereField` | `@payloadcms/next/client` |
`@payloadcms/ui` |

The `./client`, `./rsc`, and `./templates` subpath exports on
`@payloadcms/next` are removed entirely.

#### Codemod

To migrate automatically, there's a codemod for this change available by
running:

```bash
npx @payloadcms/codemod --transform migrate-next-subpath-exports
```

Introduce `@payloadcms/tanstack-start`, a framework adapter that lets
the Payload admin run on TanStack Start in addition to Next.js.

What's included:

- `packages/tanstack-start/` — the adapter package: `RouterAdapter`,
  `ServerAdapter`, auth server functions, server-function dispatcher,
  Vite plugins, layouts, and RSC entry points.
- `tanstack-app/` — minimal test harness app that boots the adapter for
  local dev and e2e runs.
- `test/adapters/tanstackStartDevServer.ts` — dev-server module the
  shared test runner will dispatch to when `PAYLOAD_FRAMEWORK=tanstack-start`.
- `dev:tanstack` / `test:e2e:tanstack[:headed]` npm scripts and
  `@payloadcms/tanstack-start` tsconfig path mapping.
- Tanstack-specific plan docs under `docs/plans/`.

This PR only contains TanStack-specific files. The framework-agnostic
abstractions that this adapter consumes (router/server contracts, the
move of admin views to `@payloadcms/ui`, `ComponentRenderer`,
`renderAdminPage` dispatcher, RSC Flight unification, dev-server test
harness abstraction) ship as separate upstream PRs — three of which
(#16753, #16763, #16765) are already merged. See
`docs/reviews/tanstack-pr-shrink-strategy.md` for the full layering and
filing order.

The branch will not build standalone until the remaining abstraction-
layer PRs land upstream.

Decouples the root layout from Next.js-specific implementation details.
This way we can consume the root layout using alternative React
frameworks, e.g. TanStack.

The root layout consumes the new [Router
Adapter](#16763) and [Server
Adapter](#16753), with
additional layers of abstraction for font loading and dependency
checking.

The framework-agnostic implementation lives in `@payloadcms/ui` and is
exposed at a new `@payloadcms/ui/layouts` entrypoint.
`@payloadcms/next/layouts` continues to work unchanged — it is now a
thin wrapper that injects the Next.js adapters, fonts, and dep-check
constraints into the ui implementation, so existing app callers need no
changes.

```tsx
import { RootLayout } from '@payloadcms/ui/layouts'

<RootLayout
  config={config}
  importMap={importMap}
  fonts={[{ className: inter.className, variable: inter.variable }]}
  RouterAdapter={MyRouterAdapter}
  serverAdapter={myServerAdapter}
  serverFunction={serverFunction}
  additionalDependencyChecks={{
    dependencyVersions: {
      'my-framework': { required: false, version: '>=1.0.0' },
    },
  }}
>
  {children}
</RootLayout>
```

Internally:

- `initReq` moves to `@payloadcms/ui/utilities/initReq` and accepts the
adapter as an explicit argument rather than reading `next/headers`
directly.
- Universal `react` / `react-dom` version checks move to
`@payloadcms/ui/utilities/checkDependencies`. Each framework adapter
layers its own constraints through the `additionalDependencyChecks` prop
— the Next.js wrapper passes `next: '>=15.0.0'`.
- The Next.js wrapper now lives at
`packages/next/src/adapters/layout.tsx`, mirroring the existing
`router.tsx` and `server.ts` adapter files.
- Language switching now dispatches through the existing
`serverFunction` mechanism via a new `switch-language` handler in
`@payloadcms/next/utilities/switchLanguageHandler`, rather than as a
dedicated `switchLanguageServerAction` prop. The handler writes the
cookie using the server adapter via `req.server.setCookie(...)`.

…er (#16884)

Removes the `ParamsProvider` and `SearchParamsProvider` from
`@payloadcms/ui`, which were deprecated in #9581 since
[v3.3.0](https://github.com/payloadcms/payload/releases/tag/v3.3.0).

The `useParams` and `useSearchParams` hooks remain available from
`@payloadcms/ui` with identical usage — they now originate from the new
[Router Adapter](#16763)
instead of these dedicated context providers. No migration steps are
needed.