Move example to genai_example

Renamed the example directory to genai_example, updated package name in pubspec.yaml, and added pubspec_overrides.yaml for local dependency overrides. Updated pubspec.lock to reflect new and overridden dependencies.

packages/genai/genai_example/pubspec.lock

@@ -1,6 +1,14 @@
 # Generated by pub
 # See https://dart.dev/tools/pub/glossary#lockfile
 packages:
+  adaptive_number:
+    dependency: transitive
+    description:
+      name: adaptive_number
+      sha256: "3a567544e9b5c9c803006f51140ad544aedc79604fd4f3f2c1380003f97c1d77"
+      url: "https://pub.dev"
+    source: hosted
+    version: "1.0.0"
   async:
     dependency: transitive
     description:
@@ -10,7 +18,7 @@ packages:
     source: hosted
     version: "2.13.0"
   better_networking:
-    dependency: transitive
+    dependency: "direct overridden"
     description:
       path: "../../better_networking"
       relative: true
@@ -48,6 +56,22 @@ packages:
       url: "https://pub.dev"
     source: hosted
     version: "1.19.1"
+  convert:
+    dependency: transitive
+    description:
+      name: convert
+      sha256: b30acd5944035672bc15c6b7a8b47d773e41e2f17de064350988c5d02adb1c68
+      url: "https://pub.dev"
+    source: hosted
+    version: "3.1.2"
+  crypto:
+    dependency: transitive
+    description:
+      name: crypto
+      sha256: "1e445881f28f22d6140f181e07737b22f1e099a5e1ff94b0af2f9e4a463f4855"
+      url: "https://pub.dev"
+    source: hosted
+    version: "3.0.6"
   cupertino_icons:
     dependency: "direct main"
     description:
@@ -56,6 +80,22 @@ packages:
       url: "https://pub.dev"
     source: hosted
     version: "1.0.8"
+  dart_jsonwebtoken:
+    dependency: transitive
+    description:
+      name: dart_jsonwebtoken
+      sha256: "21ce9f8a8712f741e8d6876a9c82c0f8a257fe928c4378a91d8527b92a3fd413"
+      url: "https://pub.dev"
+    source: hosted
+    version: "3.2.0"
+  ed25519_edwards:
+    dependency: transitive
+    description:
+      name: ed25519_edwards
+      sha256: "6ce0112d131327ec6d42beede1e5dfd526069b18ad45dcf654f15074ad9276cd"
+      url: "https://pub.dev"
+    source: hosted
+    version: "0.3.1"
   fake_async:
     dependency: transitive
     description:
@@ -80,6 +120,14 @@ packages:
       url: "https://pub.dev"
     source: hosted
     version: "7.0.1"
+  fixnum:
+    dependency: transitive
+    description:
+      name: fixnum
+      sha256: b6dc7065e46c974bc7c5f143080a6764ec7a4be6da1285ececdc37be96de53be
+      url: "https://pub.dev"
+    source: hosted
+    version: "1.1.1"
   flutter:
     dependency: "direct main"
     description: flutter
@@ -262,13 +310,20 @@ packages:
       url: "https://pub.dev"
     source: hosted
     version: "2.1.8"
-  seed:
+  pointycastle:
     dependency: transitive
     description:
-      name: seed
+      name: pointycastle
-      sha256: "0d74a46abd169c96a73d9dec4739e6623021915661beadf265e885bb1eafd214"
+      sha256: "92aa3841d083cc4b0f4709b5c74fd6409a3e6ba833ffc7dc6a8fee096366acf5"
       url: "https://pub.dev"
     source: hosted
+    version: "4.0.0"
+  seed:
+    dependency: "direct overridden"
+    description:
+      path: "../../seed"
+      relative: true
+    source: path
     version: "0.0.3"
   shared_preferences:
     dependency: transitive

packages/genai/genai_example/pubspec.yaml

@@ -1,8 +1,8 @@
-name: example
+name: genai_example
 description: "A new Flutter project."
 # The following line prevents the package from being accidentally published to
 # pub.dev using `flutter pub publish`. This is preferred for private packages.
-publish_to: 'none' # Remove this line if you wish to publish to pub.dev
+publish_to: "none" # Remove this line if you wish to publish to pub.dev
 
 # The following defines the version and build number for your application.
 # A version number is three numbers separated by dots, like 1.2.43
@@ -53,7 +53,6 @@ dev_dependencies:
 
 # The following section is specific to Flutter packages.
 flutter:
-
   # The following line ensures that the Material Icons font is
   # included with your application, so that you can use the icons in
   # the material Icons class.

packages/genai/genai_example/pubspec_overrides.yaml

@@ -0,0 +1,8 @@
+# melos_managed_dependency_overrides: better_networking,genai,seed
+dependency_overrides:
+  better_networking:
+    path: ../../better_networking
+  genai:
+    path: ..
+  seed:
+    path: ../../seed