Add CI to build the website on PR

[ksunden]

We recently merged a change that broke the build and did not realize it until the deploy action was run. A PR scoped build would go a long way to making sure the build isn't broken.

Most ideally we would be able to see the results, this could be as an artifact that we would need to download or somehow serving (we do the latter in mpl, but it is more complicated and involves circleCI because doing so with GHA does not provide the tools needed, I belieive... a zip archive/tarball of the public folder is probably sufficient. Mostly I care about the logs from the build process and getting red CI.