feat(skilltree): connect web app to backend API

- Add API client for backend communication
- Add skills and activities API modules
- Add auth store with Mana Core Auth integration
- Update skills store to use API when authenticated
- Keep IndexedDB as offline fallback
- Add hooks.server.ts for runtime env injection

https://claude.ai/code/session_015XCsTDS9aLZ64Zin4HU6ex

apps/skilltree/apps/web/package.json

@@ -25,6 +25,7 @@
 		"vite": "^6.0.0"
 	},
 	"dependencies": {
+		"@manacore/shared-auth": "workspace:*",
 		"@manacore/shared-tailwind": "workspace:*",
 		"@manacore/shared-theme": "workspace:*",
 		"@manacore/shared-utils": "workspace:*",