Catch errors from the TS type checker in the examples category

[lhstrh]

Currently, examples are only validated, not build. This means that certain errors (like type errors unveiled by running tsc) remain hidden.

[lhstrh]

The reason for this, however, is that it's not always straightforward to build examples due to complicated dependencies and possible platform dependence. We can tailor our testing to examples once we have factored them out into their own repository, which is what we should prioritize instead of fixing this.