chore(pkglint): require jsii.dotnet.packageId in package.json (#25816)

Guards against the following error when creating new packages:

```bash
Error: The module @aws-cdk/app-staging-synthesizer-alpha does not have a dotnet.packageId setting
```

----

*By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license*

Author: kaizencc

tools/@aws-cdk/pkglint/lib/rules.ts

@@ -910,6 +910,7 @@ function cdkModuleName(name: string) {
     javaPackage: `software.amazon.awscdk${isLegacyCdkPkg ? '' : `.${suffix.replace(/aws-/, 'services-').replace(/-/g, '.')}`}`,
     mavenArtifactId,
     dotnetNamespace: `Amazon.CDK${isCdkPkg ? '' : `.${dotnetSuffix}`}`,
+    dotnetPackageId: `Amazon.CDK${isCdkPkg ? '' : `.${dotnetSuffix}`}`,
     python: {
       distName: `aws-cdk.${pythonName}`,
       module: `aws_cdk.${pythonName.replace(/-/g, '_')}`,
@@ -926,10 +927,6 @@ export class JSIIDotNetNamespaceIsRequired extends ValidationRule {
   public validate(pkg: PackageJson): void {
     if (!isJSII(pkg)) { return; }
 
-    // skip the legacy @aws-cdk/cdk because we actually did not rename
-    // the .NET module, so we are not publishing the deprecated one
-    if (pkg.packageName === '@aws-cdk/cdk') { return; }
-
     const dotnet = deepGet(pkg.json, ['jsii', 'targets', 'dotnet', 'namespace']) as string | undefined;
     const moduleName = cdkModuleName(pkg.json.name);
     expectJSON(this.name, pkg, 'jsii.targets.dotnet.namespace', moduleName.dotnetNamespace, /\./g, /*case insensitive*/ true);
@@ -949,7 +946,34 @@ export class JSIIDotNetNamespaceIsRequired extends ValidationRule {
 }
 
 /**
- * JSII .NET namespace is required and must look sane
+ * JSII .NET packageId is required and must look sane
+ */
+export class JSIIDotNetPackageIdIsRequired extends ValidationRule {
+  public readonly name = 'jsii/dotnet';
+
+  public validate(pkg: PackageJson): void {
+    if (!isJSII(pkg)) { return; }
+
+    const dotnet = deepGet(pkg.json, ['jsii', 'targets', 'dotnet', 'namespace']) as string | undefined;
+    const moduleName = cdkModuleName(pkg.json.name);
+    expectJSON(this.name, pkg, 'jsii.targets.dotnet.packageId', moduleName.dotnetPackageId, /\./g, /*case insensitive*/ true);
+
+    if (dotnet) {
+      const actualPrefix = dotnet.split('.').slice(0, 2).join('.');
+      const expectedPrefix = moduleName.dotnetPackageId.split('.').slice(0, 2).join('.');
+      if (actualPrefix !== expectedPrefix) {
+        pkg.report({
+          ruleName: this.name,
+          message: `.NET packageId must share the first two segments of the default namespace, '${expectedPrefix}' vs '${actualPrefix}'`,
+          fix: () => deepSet(pkg.json, ['jsii', 'targets', 'dotnet', 'packageId'], moduleName.dotnetPackageId),
+        });
+      }
+    }
+  }
+}
+
+/**
+ * JSII .NET icon url is required and must look sane
  */
 export class JSIIDotNetIconUrlIsRequired extends ValidationRule {
   public readonly name = 'jsii/dotnet/icon-url';