chore: remove 'ubergen exclude' from example package (#19177)

The example construct library package comes with
`ubergen { exclude: true }` configured by default. We do want new construct
libraries included into ubergen by default, though.

I got into a little fight with `pkglint`: it said that `private` packages must always have `ubergen: exclude` set, but this package should be private but not have the `exclude` flag set.

Seems simpler to just exclude private packages from ubergen by default, without the middle man of the `exclude` flag.

----

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

packages/@aws-cdk/example-construct-library/package.json

@@ -111,8 +111,5 @@
     "env": {
       "AWSLINT_BASE_CONSTRUCT": true
     }
-  },
-  "ubergen": {
-    "exclude": true
   }
 }

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

@@ -1733,18 +1733,6 @@ export class UbergenPackageVisibility extends ValidationRule {
           },
         });
       }
-    } else {
-      if (pkg.json.private && !pkg.json.ubergen?.exclude) {
-        pkg.report({
-          ruleName: this.name,
-          message: 'ubergen.exclude must be configured for private packages',
-          fix: () => {
-            pkg.json.ubergen = {
-              exclude: true,
-            };
-          },
-        });
-      }
     }
   }
 }

tools/@aws-cdk/ubergen/bin/ubergen.ts

@@ -129,7 +129,7 @@ async function findLibrariesToPackage(uberPackageJson: PackageJson): Promise<rea
   for (const dir of await fs.readdir(librariesRoot)) {
     const packageJson = await fs.readJson(path.resolve(librariesRoot, dir, 'package.json'));
 
-    if (packageJson.ubergen?.exclude) {
+    if (packageJson.private || packageJson.ubergen?.exclude) {
       console.log(`\t⚠️ Skipping (ubergen excluded):   ${packageJson.name}`);
       continue;
     } else if (packageJson.jsii == null ) {