refactor [NET-1644]: Clean-up tsconfigs for the browser-test-runner package

[mondoreale]

This pull request updates the TypeScript configuration for the browser-test-runner package to simplify build scripts and consolidate configuration. The main changes are the removal of the local tsconfig.node.json in favor of a single tsconfig.json, and updates to related build and linting settings.

TypeScript configuration consolidation:

• Added a new tsconfig.json that extends the root configuration and specifies output and included files, replacing the previous local tsconfig.node.json.
• Updated ESLint configuration to reference the new tsconfig.json instead of tsconfig.node.json.

Build and script improvements:

• Simplified the build script in package.json to use the default TypeScript project and added a new check script for type checking.

[linear]

NET-1644 Clean-up `browser-test-runner` package tsconfigs