feat(frontend/auth): fix cookie not working due to path being /app

Cookies being set to path=/app meant that the API didn't have those
cookies.
Also fixed the Schema injection for auth'ed routes

frontend/pnpm-lock.yaml

@@ -11,6 +11,9 @@ importers:
       '@tailwindcss/vite':
         specifier: ^4.1.16
         version: 4.1.16(vite@7.1.12(jiti@2.6.1)(lightningcss@1.30.2))
+      js-cookie:
+        specifier: ^3.0.5
+        version: 3.0.5
       openapi-fetch:
         specifier: ^0.15.0
         version: 0.15.0
@@ -18,6 +21,9 @@ importers:
         specifier: ^4.1.16
         version: 4.1.16
     devDependencies:
+      '@types/js-cookie':
+        specifier: ^3.0.6
+        version: 3.0.6
       typescript:
         specifier: ~5.9.3
         version: 5.9.3
@@ -405,6 +411,9 @@ packages:
   '@types/estree@1.0.8':
     resolution: {integrity: sha512-dWHzHa2WqEXI/O1E9OjrocMTKJl2mSrEolh1Iomrv6U+JuNwaHXsXx9bLu5gG7BUWFIN0skIQJQ/L1rIex4X6w==}
 
+  '@types/js-cookie@3.0.6':
+    resolution: {integrity: sha512-wkw9yd1kEXOPnvEeEV1Go1MmxtBJL0RR79aOTAApecWFVu7w0NNXNqhcWgvw2YgZDYadliXkl14pa3WXw5jlCQ==}
+
   debug@4.4.3:
     resolution: {integrity: sha512-RGwwWnwQvkVfavKVt22FGLw+xYSdzARwm0ru6DhTVA3umU5hZc28V3kO4stgYryrTlLpuvgI9GiijltAjNbcqA==}
     engines: {node: '>=6.0'}
@@ -451,6 +460,10 @@ packages:
     resolution: {integrity: sha512-ekilCSN1jwRvIbgeg/57YFh8qQDNbwDb9xT/qu2DAHbFFZUicIl4ygVaAvzveMhMVr3LnpSKTNnwt8PoOfmKhQ==}
     hasBin: true
 
+  js-cookie@3.0.5:
+    resolution: {integrity: sha512-cEiJEAEoIbWfCZYKWhVwFuvPX1gETRYPw6LlaTKoxD3s2AkXzkCjnp6h0V77ozyqj0jakteJ4YqDJT830+lVGw==}
+    engines: {node: '>=14'}
+
   lightningcss-android-arm64@1.30.2:
     resolution: {integrity: sha512-BH9sEdOCahSgmkVhBLeU7Hc9DWeZ1Eb6wNS6Da8igvUwAe0sqROHddIlvU06q3WyXVEOYDZ6ykBZQnjTbmo4+A==}
     engines: {node: '>= 12.0.0'}
@@ -867,6 +880,8 @@ snapshots:
 
   '@types/estree@1.0.8': {}
 
+  '@types/js-cookie@3.0.6': {}
+
   debug@4.4.3:
     dependencies:
       ms: 2.1.3
@@ -920,6 +935,8 @@ snapshots:
 
   jiti@2.6.1: {}
 
+  js-cookie@3.0.5: {}
+
   lightningcss-android-arm64@1.30.2:
     optional: true