fix(studio): make dev:studio-local work with the tanstack dev server (#48090)

With `STUDIO_FRAMEWORK=tanstack`, `pnpm dev:studio-local` ran Studio in
platform mode against the management API instead of the local CLI stack
(`/` redirected to `/org` instead of `/project/default`). Vite selects
env files by *mode* while the Next dev server selects them via
`NODE_ENV=test`, so the tanstack dev server never loaded `.env.test` and
the developer's `.env.local` (`NEXT_PUBLIC_IS_PLATFORM="true"`) won. The
shell `NODE_ENV=test` also gets inlined into the dev client bundle by
Vite, flipping `API_URL` to the vitest-only MSW host.

`vite dev --mode test` isn't a viable fix: TanStack Start's dev-server
plugin treats mode `test` as "running under vitest" and skips installing
its SSR middleware, so every route 404s. Instead, dev keeps mode
`development` and overlays the env cascade named by `MODE` on top.

**Changed:**
- `dev:studio-local` now also sets `MODE=test` (the same knob
`build:tanstack` / `e2e:setup:selfhosted` already use)
- `vite.config.ts` dev server: loads the `MODE`-named env cascade for
the `NEXT_PUBLIC_*` client defines and seeds it into `process.env` for
SSR, without clobbering shell-provided values (matching `serve.js`
semantics, and safe against TanStack's own load-env plugin since
`loadEnv` gives existing `process.env` priority)
- `vite.config.ts` dev server: remaps a shell `NODE_ENV=test` to
`development` so it can't be baked into the client bundle (mirrors `next
dev` behavior)

Platform-mode `pnpm dev:studio` sets no `MODE`, so the overlay is a
no-op there. Build (`--mode test`), `serve.js`, and vitest (separate
`vitest.config`) paths are unchanged.

## To test

- `supabase` CLI installed, then: `STUDIO_FRAMEWORK=tanstack pnpm
dev:studio-local`
- Visit http://localhost:8082 — it should redirect to `/project/default`
(not `/org`) and the Default Project page should load with data from the
local stack (network requests go to `localhost:8082/api/platform/...`,
no `api.supabase.(com|green)` calls)
- `pnpm dev:studio` (platform mode, tanstack) still behaves as before —
redirects to `/org`
- Next path regression check: plain `pnpm dev:studio-local` (no
`STUDIO_FRAMEWORK`) still works

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

## Summary by CodeRabbit

* **Bug Fixes**
* Improved local Studio development and test-mode environment handling.
* Prevented test settings from being incorrectly embedded in the client
application.
* Ensured environment values are loaded consistently across development
and test scenarios.

* **Chores**
* Updated the local Studio development command to explicitly use test
mode.

<!-- end of auto-generated comment: release notes by coderabbit.ai -->

Co-authored-by: Alaister Young <10985857+alaister@users.noreply.github.com>

package.json

@@ -15,7 +15,7 @@
     "clean": "turbo run clean --parallel && rimraf -G node_modules/{*,.bin,.modules.yaml} .turbo/cache",
     "dev": "turbo run dev --parallel",
     "dev:studio": "turbo run dev --filter=studio --parallel",
-    "dev:studio-local": "pnpm setup:cli && NODE_ENV=test pnpm --prefix ./apps/studio dev",
+    "dev:studio-local": "pnpm setup:cli && NODE_ENV=test MODE=test pnpm --prefix ./apps/studio dev",
     "dev:docs": "turbo run dev --filter=docs --parallel",
     "dev:www": "turbo run dev --filter=www --parallel",
     "dev:design-system": "turbo run dev --filter=design-system --parallel",