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build(studio): Next-compat shims (stack 2/6, from #46424) (#47110)

**Stack 2/6** of the TanStack Start migration (#46424). Stacked on
**#47107** (S1) — review that first; this PR's diff is just the compat
shims.

> [!NOTE]
> Purely additive. Next never imports these files — under TanStack
they're wired in via Vite aliases (`next/*` → `@/compat/next/*`). No
routes consume them yet (that begins in stack 3).

## What's in this PR
`apps/studio/compat/next/*` — drop-in shims so the existing pages-router
code runs unchanged under TanStack Start:
- `link`, `router`, `navigation`, `head`, `image`, `legacy/image`,
`script`, `dynamic`, `server`, `_router-events` — React/runtime shims
over `@tanstack/react-router`.
- `api.ts` — `toWebHandler`, which adapts a pages-router API handler
`(req, res)` into a TanStack server-route Web `fetch` handler.

## Verification
On top of S1: `studio` typecheck ✓, lint (0 errors) ✓. Next build is
unaffected (nothing imports these under tsc).


<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

* **New Features**
* Added broad Next.js compatibility support for routing, links, dynamic
imports, images, scripts, head metadata, navigation hooks, server
responses, and API handlers.
* Improved handling of redirects, pathname/search params, base paths,
and event callbacks for smoother app behavior.

* **Tests**
* Added coverage for URL resolution and dynamic route interpolation to
verify Next-style routing behavior.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

---------

Co-authored-by: Alaister Young <10985857+alaister@users.noreply.github.com>
Co-authored-by: Ivan Vasilov <vasilov.ivan@gmail.com>

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