Run TypeScript type checking alongside the current build process to provide errors to the user

[FrederikBolding]

Currently the CLI doesn't inform the user of typing errors in TypeScript input and builds successfully even with typing errors. Instead we should probably show the typing errors to the user.

Potentially we could add a flag to skip the errors and build regardless.

This happens because we use a Babel plugin for TypeScript support, which simply strips the types without checking them. Instead, we should probably run TypeScript type checking (without emitting) alongside our build process.