chore(studio): support NEXT_PUBLIC_BASE_PATH and port / redirect

Wire Vite `base`, Nitro `baseURL`, and the TanStack router `basepath` off
the same `NEXT_PUBLIC_BASE_PATH` env var so the prefix stays in sync (all
three layers are required — there's no single knob in TanStack Start).
Defaults are unchanged when the var is empty.

Also replace the `/` placeholder with the redirect rules that used to live
in `next.config.ts`'s `redirects()`: platform → `/org` (or
`/new/new-project` when deep-linked with `?next=new-project`), self-hosted
→ `/project/default`. Kept as a route (not a Nitro `routeRule`) so it
works in `vite dev` and can branch on the query param.

apps/studio/router.tsx

@@ -23,6 +23,10 @@ export function getRouter() {
     context,
     scrollRestoration: true,
     defaultPreload: 'intent',
+    // Inlined via Vite's `define` at build time; stays undefined (= app at `/`)
+    // unless NEXT_PUBLIC_BASE_PATH is set. Must agree with Vite `base` and
+    // Nitro `baseURL` — see vite.config.ts.
+    basepath: process.env.NEXT_PUBLIC_BASE_PATH || undefined,
   })
 
   setupRouterSsrQueryIntegration({ router, queryClient: context.queryClient })

apps/studio/routes/index.tsx

@@ -1,9 +1,28 @@
-import { createFileRoute } from '@tanstack/react-router'
+import { createFileRoute, redirect } from '@tanstack/react-router'
 
+import { IS_PLATFORM } from '@/lib/constants'
+
+// `/` is never rendered — it always redirects. Mirrors the Next.js
+// `redirects()` rules in next.config.ts: platform sends users to `/org`
+// (or `/new/new-project` when deep-linked with `?next=new-project`),
+// self-hosted sends them straight to `/project/default`.
+//
+// Kept as a route (rather than a Nitro `routeRule`) so the redirect works
+// in both `vite dev` and prod — `routeRules` only fire under Nitro — and
+// so the query-param branch has somewhere to run.
 export const Route = createFileRoute('/')({
-  component: RouteComponent,
+  validateSearch: (search: Record<string, unknown>) => ({
+    next: typeof search.next === 'string' ? search.next : undefined,
+  }),
+  beforeLoad: ({ search }) => {
+    // `href` instead of `to` because these targets aren't in the TanStack
+    // routeTree yet — they're still on the Next.js pages side during the
+    // migration. Swap to `to` once `/org`, `/new/new-project`, and
+    // `/project/default` are migrated.
+    if (IS_PLATFORM) {
+      if (search.next === 'new-project') throw redirect({ href: '/new/new-project' })
+      throw redirect({ href: '/org' })
+    }
+    throw redirect({ href: '/project/default' })
+  },
 })
-
-function RouteComponent() {
-  return <div>Hello "/"!</div>
-}

apps/studio/vite.config.ts

@@ -88,6 +88,16 @@ export default defineConfig(({ mode }) => {
       .map(([key, value]) => [`process.env.${key}`, JSON.stringify(value)])
   )
 
+  // Mirror Next's `basePath` via NEXT_PUBLIC_BASE_PATH. Unlike Next, TanStack
+  // Start has no single knob — the prefix has to be declared in three places
+  // (see BASE_PATH_REDIRECT_GUIDE.md):
+  //   - Vite `base`      — bakes the prefix into asset URLs in the built bundle
+  //   - Nitro `baseURL`  — mounts the production server at that path
+  //   - Router `basepath` — makes client-side navigation match the prefix
+  // The router layer is set in router.tsx off the same env var (inlined via
+  // `define` above). Leaving the var empty keeps the app at `/` as today.
+  const basePath = env.NEXT_PUBLIC_BASE_PATH || undefined
+
   return {
     server: {
       port: 3000,
@@ -95,6 +105,7 @@ export default defineConfig(({ mode }) => {
     resolve: {
       tsconfigPaths: true,
     },
+    ...(basePath && { base: basePath }),
     define: publicEnvDefines,
     ssr: {
       // `lodash` is CJS; its named-export interop fails in Node ESM unless bundled.
@@ -131,6 +142,11 @@ export default defineConfig(({ mode }) => {
         // `modules/index.js` via `package.json#exports`) out of the picture.
         exportConditions: ['module'],
         noExternals: ['tslib'],
+        // See the `basePath` comment above — Nitro's own mount point needs the
+        // same prefix as Vite/router. `routeRules` paths are matched AFTER
+        // baseURL is stripped, so if we add redirects later they should be
+        // written relative to the base.
+        ...(basePath && { baseURL: basePath }),
       }),
       viteReact(),
     ],