The action installs the latest typescript which was causing a CDK deploy failure on my end with:
Debug Failure. False expression: Non-string value passed to ts.resolveTypeReferenceDirective, likely by a wrapping package working with an outdated resolveTypeReferenceDirectives signature. This is probably not a problem in TS itself.
Testing locally passed until I tried with the latest version of typescript which also failed. Please consider adding a parameter for preferred TS version similar to CDK version to install.