I have been meaning to use Justine's RedBean to build a "project app" (kind of like what the OP describes, but leaning more towards something like Datasette). It would contain the data, the paper(s), and the UI for interacting with the data (and supporting scripts or R that can be run with other tools). I just like the idea of a portable single-file scientific artifact.

(also another call for jart to fix their certs!)