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feat(studio): TanStack project routes — data surfaces (stack 5.1/6, from #46424) (#47117)

**Stack 5.1/6** of the TanStack Start migration (#46424). The original
S5 (174 files) was over CodeRabbit's 150-file review cap, so it's split
into 5.1 + 5.2 by product. Stacked on **#47113** (S4).

> [!NOTE]
> Thin route wrappers rendering the existing pages-router components via
compat shims. Next-safe (full Next build run). The TanStack app isn't
functional end-to-end until 5.2 + the matrix flip.

## What's in this PR
- **Data-cluster project routes:** database, editor, sql, storage,
realtime, branches.
- **Top-level / onboarding routes:** `authorize`, `join`, `logout`,
`redeem`, `verify-email`, `claim-project`, aws-marketplace,
Vercel/GitHub integration entrypoints; `_app`/`_auth` layout shells;
`/org/_` + `/project/_` catch-alls.
- **Supporting edits:** hoist `BranchesPageWrapper` out of `getLayout`,
`ConnectStepsSection` `import.meta.glob`, `api/server.js`.
- `routeTree.gen.ts` regenerated for the routes present so far.

## Verification
On top of S1–S4: `studio` typecheck ✓, lint (0 errors) ✓, **Next build ✓
(181/181 pages)**.


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

* **Refactor**
* Restructured application routing infrastructure for improved code
organization and maintainability.
* Extracted and refactored layout wrapper components for enhanced
reusability across different sections of the application.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

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

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