Ensure non `/assets/` files can be served.

Previously, any files in `public/` (outside of `public/assets/`) would not be served up as it was assumed to match history API requests and redirect to `/index.html`.

This commit fixes that, by serving up any files that exist in the built output directory before falling back to checking for history API support (and subsequently proxying).

Closes #1404.

This is a prerequisite for #1542.