Fix Vercel API breaking change (#1883)

Fixes https://github.com/dyad-sh/dyad/issues/1652

This is kind of a hack because the Vercel SDK has a bug since their API
has subtly made a breaking change in the last month or so and the Vercel
SDK still hasn't been updated
https://github.com/vercel/sdk/issues/175#issuecomment-3608968116

Note: the Vercel SDK upgrade in this PR doesn't actually fix the issue,
but is probably good to do anyways.

<!-- This is an auto-generated description by cubic. -->
---
## Summary by cubic
Works around a breaking change in Vercel’s API by bypassing the SDK for
project queries. Restores listing, availability checks, and project
linking.

- **Bug Fixes**
  - Added a direct HTTP call to GET /v9/projects using the Vercel token.
- Replaced SDK calls in list, name availability, and connect-to-project
flows.
- Added minimal types and clearer error handling for project responses.

- **Dependencies**
- Bumped @vercel/sdk to 1.18.0. The upgrade doesn’t fix the bug but is
safe to adopt.

<sup>Written for commit 306af5c3f235f0ab9d87c809bb8cf54016a5d59f.
Summary will update automatically on new commits.</sup>

<!-- End of auto-generated description by cubic. -->

<!-- CURSOR_SUMMARY -->
---

> [!NOTE]
> Replaces Vercel project retrieval with a direct HTTP helper used
across handlers to handle API changes, and updates @vercel/sdk to
^1.18.0.
> 
> - **IPC/Backend (Vercel)**:
> - Add `getVercelProjects` helper to fetch projects via `GET
/v9/projects`, mimicking `vercel.projects.getProjects`.
>   - Update handlers to use the new helper:
>     - `vercel:list-projects` (`handleListVercelProjects`)
>     - `vercel:is-project-available` (`handleIsProjectAvailable`)
> - `vercel:connect-existing-project` (`handleConnectToExistingProject`)
> - Add lightweight types: `VercelProjectResponse`,
`GetVercelProjectsResponse`.
> - **Dependencies**:
>   - Bump `@vercel/sdk` to `^1.18.0`.
> 
> <sup>Written by [Cursor
Bugbot](https://cursor.com/dashboard?tab=bugbot) for commit
306af5c3f235f0ab9d87c809bb8cf54016a5d59f. This will update automatically
on new commits. Configure
[here](https://cursor.com/dashboard?tab=bugbot).</sup>
<!-- /CURSOR_SUMMARY -->

package.json

@@ -124,7 +124,7 @@
     "@tanstack/react-query": "^5.75.5",
     "@tanstack/react-router": "^1.114.34",
     "@types/uuid": "^10.0.0",
-    "@vercel/sdk": "^1.10.0",
+    "@vercel/sdk": "^1.18.0",
     "@vitejs/plugin-react": "^4.3.4",
     "ai": "^5.0.15",
     "better-sqlite3": "^12.4.1",