refactor: move system health procedure from system to admin router

- Rename `system.health` → `admin.systemHealth` and gate it behind the admin middleware
- Remove `tmdbConfigured` from `system.status` response; update description to reflect its purpose
- Update all call sites on web and native to use `orpc.admin.systemHealth`
- Rename and relocate the docs page from `system/system.health.mdx` to `admin/admin.systemHealth.mdx`

packages/api/src/contract.ts

@@ -406,23 +406,12 @@ export const contract = {
         method: "GET",
         path: "/system/status",
         tags: ["System"],
-        summary: "Get system status",
+        summary: "Get internal system config",
         description:
-          "Quick check of whether TMDB is configured. Does not require authentication.",
-        successDescription: "TMDB configuration status",
+          "Returns internal configuration such as the public API URL. Requires authentication.",
+        successDescription: "Internal system configuration",
       })
       .output(SystemStatusOutput),
-    health: oc
-      .route({
-        method: "GET",
-        path: "/system/health",
-        tags: ["System"],
-        summary: "Get system health report",
-        description:
-          "Comprehensive health check covering database, TMDB connectivity, cron jobs, image cache, backups, and environment. Admin only.",
-        successDescription: "Full system health report",
-      })
-      .output(SystemHealthOutput),
   },
   integrations: {
     list: oc
@@ -653,6 +642,17 @@ export const contract = {
       })
       .input(z.void())
       .output(PurgeImageCacheOutput),
+    systemHealth: oc
+      .route({
+        method: "GET",
+        path: "/admin/system-health",
+        tags: ["Admin"],
+        summary: "Get system health report",
+        description:
+          "Comprehensive health check covering database, TMDB connectivity, cron jobs, image cache, backups, and environment.",
+        successDescription: "Full system health report",
+      })
+      .output(SystemHealthOutput),
   },
   account: {
     updateName: oc

packages/api/src/schemas.ts

@@ -884,12 +884,11 @@ export const SystemHealthSchema = z
 
 export const SystemStatusOutput = z
   .object({
-    tmdbConfigured: z
-      .boolean()
-      .describe("Whether a TMDB API token is configured"),
     publicApiUrl: z.string().describe("Base URL of the centralized public API"),
   })
-  .meta({ description: "Quick TMDB configuration check" });
+  .meta({
+    description: "Internal system configuration for authenticated clients",
+  });
 
 export const SystemHealthOutput = SystemHealthSchema;