Add shared package: types, schemas, plans and API client

Holds everything web, mobile and API must agree on: DTOs, zod input
schemas, plan entitlements (the single place feature gates live),
streaming-service link helpers, feed ordering and a typed API client.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01MzFywujuH9TiuXbr9vjoX8

packages/shared/tsconfig.json

@@ -0,0 +1,12 @@
+{
+  "extends": "../../tsconfig.base.json",
+  "include": [
+    "src"
+  ],
+  "compilerOptions": {
+    "lib": [
+      "ES2023",
+      "DOM"
+    ]
+  }
+}