[Tool] Add ability to check dependencies independently of dev-dependencies, exclude integration_test from dependencies (#6446)

Create a linter that ensures that `integration_test` is not used in dependencies. 

Will be paired with a change to documentation 
```
If you are considering adding an external dependency:

Consider other options, and discuss with #hackers-ecosystem in Discord.
* If you add a dev_dependency on an external package, pin it to a specific version if at all possible.
* If you add a dependency on an external package in an example/, pin it to a specific version if at all possible.
* Some dependencies should only be linked as dev dependencies like integration_test 
```

Related to flutter/flutter/issues/145992

script/tool/lib/src/pubspec_check_command.dart

@@ -356,7 +356,7 @@ class PubspecCheckCommand extends PackageLoopingCommand {
             'a topic. Add "$topicName" to the "topics" section.';
       }
     }
-    
+
     // Validates topic names according to https://dart.dev/tools/pub/pubspec#topics
     final RegExp expectedTopicFormat = RegExp(r'^[a-z](?:-?[a-z0-9]+)*$');
     final Iterable<String> invalidTopics = topics.where((String topic) =>
@@ -542,6 +542,7 @@ class PubspecCheckCommand extends PackageLoopingCommand {
   // there are any that aren't allowed.
   String? _checkDependencies(Pubspec pubspec) {
     final Set<String> badDependencies = <String>{};
+    // Shipped dependencies.
     for (final Map<String, Dependency> dependencies
         in <Map<String, Dependency>>[
       pubspec.dependencies,
@@ -553,6 +554,19 @@ class PubspecCheckCommand extends PackageLoopingCommand {
         }
       });
     }
+
+    // Ensure that dev-only dependencies aren't in `dependencies`.
+    const List<String> devOnlyDependencies = <String>['integration_test'];
+    // Non-published packages like pidgeon subpackages are allowed to violate
+    // the dev only dependencies rule.
+    if (pubspec.publishTo != 'none') {
+      pubspec.dependencies.forEach((String name, Dependency dependency) {
+        if (devOnlyDependencies.contains(name)) {
+          badDependencies.add(name);
+        }
+      });
+    }
+
     if (badDependencies.isEmpty) {
       return null;
     }
@@ -563,6 +577,7 @@ class PubspecCheckCommand extends PackageLoopingCommand {
   }
 
   // Checks whether a given dependency is allowed.
+  // Defaults to false.
   bool _shouldAllowDependency(String name, Dependency dependency) {
     if (dependency is PathDependency || dependency is SdkDependency) {
       return true;