Add typecheck for e2e tests (#44788)

* Add typecheck for e2e workspaces

* Fix TS errors

* Add changelog

* Add e2e and tools for typechecking

* FIx tsconfig for super-cache

Committed via a GitHub action: https://github.com/Automattic/jetpack/actions/runs/16961822769

Upstream-Ref: Automattic/jetpack@bb379a2

Author: manzoorwanijk

CHANGELOG.md

@@ -9,6 +9,9 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 This is an alpha version! The changes listed here are not final.
 
+### Added
+- Added typecheck support for E2E tests.
+
 ### Changed
 - Update package dependencies.