[FEATURE REQUEST] Build and Test via Github Actions

Would be nice if each PR triggered a build and test of the branch. That way it would be a bit more robust, and less likely to let through bugs that crash the site. Especially useful for dependency updates.

As referenced here:
> > @Panquesito7 did you test it locally? Also, did you see the changelog?
>
> I haven't tested it locally (we could use Gitpod to deploy the page, though). The changelog or commits seem to be to fix a security issue. https://github.com/devicons/devicon/security/dependabot/6

No need to deploy imo. Just a simple build and run would suffice. If it runs, and the code checks are all green, it probably should work.

We could add a build step to the CodeQL workflow though. Maybe just add `npm ci`, `npm build` and `npm test`?
Can probably just be added as a replacement of these lines: https://github.com/devicons/devicon/blob/1119b9f84c0290e0f0b38982099a2bd027a48bf1/.github/workflows/codeql-analysis.yml#L45-L55

_Originally posted by @Snailedlt in https://github.com/devicons/devicon/issues/1385#issuecomment-1254783495_