chore(toolkit): synth action with tests (aws#32971)

### Issue 

Closes aws#32940 

### Description of changes

Define the API for the synth action. Includes DX improvements for some other APIs.

### Describe any new or updated permissions being added

n/a

### Description of how you validated changes

These are the tests!

### Checklist
- [x] My code adheres to the [CONTRIBUTING GUIDE](https://github.com/aws/aws-cdk/blob/main/CONTRIBUTING.md) and [DESIGN GUIDELINES](https://github.com/aws/aws-cdk/blob/main/docs/DESIGN_GUIDELINES.md)

----

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

Author: mrgrain

aws-cdk.code-workspace

@@ -31,6 +31,7 @@
         "name": "aws-custom-resource-sdk-adapter",
         "rootPath": "packages/@aws-cdk/aws-custom-resource-sdk-adapter"
       },
+      { "name": "toolkit", "rootPath": "packages/@aws-cdk/toolkit" },
       { "name": "user-input-gen", "rootPath": "tools/@aws-cdk/user-input-gen" }
     ]
   },

packages/@aws-cdk/toolkit/.gitignore

@@ -26,6 +26,10 @@ build-info.json
 lib/**/*.wasm
 lib/**/*.yaml
 
+# Include test resources
+!test/_fixtures/**/app.js
+!test/_fixtures/**/cdk.out
+
 # Include config files
 !.eslintrc.js
 !jest.config.js