fix(lambda-nodejs): local tsc detection with pre compilation (#19266)

The package name is `typescript`, the bin is `tsc`.

Closes #19242


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

Author: jogold

packages/@aws-cdk/aws-lambda-nodejs/lib/bundling.ts

@@ -89,7 +89,7 @@ export class Bundling implements cdk.BundlingOptions {
     this.packageManager = PackageManager.fromLockFile(props.depsLockFilePath, props.logLevel);
 
     Bundling.esbuildInstallation = Bundling.esbuildInstallation ?? PackageInstallation.detect('esbuild');
-    Bundling.tscInstallation = Bundling.tscInstallation ?? PackageInstallation.detect('tsc');
+    Bundling.tscInstallation = Bundling.tscInstallation ?? PackageInstallation.detect('typescript');
 
     this.projectRoot = props.projectRoot;
     this.relativeEntryPath = path.relative(this.projectRoot, path.resolve(props.entry));

packages/@aws-cdk/aws-lambda-nodejs/test/bundling.test.ts

@@ -16,6 +16,7 @@ beforeEach(() => {
   jest.resetAllMocks();
   jest.restoreAllMocks();
   Bundling.clearEsbuildInstallationCache();
+  Bundling.clearTscInstallationCache();
 
   jest.spyOn(Code, 'fromAsset');
 
@@ -602,6 +603,8 @@ test('esbuild bundling with pre compilations', () => {
       ],
     }),
   });
+
+  expect(detectPackageInstallationMock).toHaveBeenCalledWith('typescript');
 });
 
 test('throws with pre compilation and not found tsconfig', () => {