There was such a journal for machine learning:
https://distill.pub/about/. But it was put on indefinite hiatus due to burnout of the editorial team.
Format problem
Perhaps most generally you have the problem of choosing a format. LaTeX is the standard in mathematics, but it is not suited for interactivity. This immediately puts you into the position of having to use non-standard tools to create your paper. Using non-standard tools generally leads to more effort.
For example you might decide to use html
as it is very suited for interactivity, but then you have to figure out how you
- cite stuff (as most of the citation machinery,
bibtex
or biblatex
is geared towards LaTeX). Of course you could do citations manually but then you have a ton of extra work.
- how to actually write equations. Html doesn't have machinery for maths, so you will end up either with MathML (would not recommended) or MathJax, KaTeX-like javascript libraries. Dealing with that is overhead.
- how you convert it back to pdf to get a journal to accept it (which then also means you have to be able to style it for the journal. And the journal typically expects LaTeX so it will at best provide
.sty
files for tex)
- ...
Distill wrote some javascript code to enable citing, but it is mixed up with their format and should probably be factored out as a standalone library. I started an attempt once to create such a citation library (bibcite) but abandoned it (due to time constraints). It is working somewhat, but does not look good, links are broken at the moment and I never got around to creating hover overs.
Related projects
LaTeXML is an attempt to convert LaTeX to html automatically (their goal is to convert the entire arxiv to html cf. ar5iv.org). It is relatively brittle in my experience, and it is limited in the interactivity department as the origin is static latex (you can hook into it to make it add javascript though, for simple stuff like collapisble proofs).
PreTeXt takes the other route, you have to write xml (which can then be converted into both LaTeX and html). People use it mostly for books (e.g. Discrete Mathematics) the styling and layout looks a bit dated, but that could be fixed and they have good support for interactivity. But they also have a custom cite style which does not work well with citation libraries like Zotero, which might be the reason people stay away from it for papers. At least I don't know of any papers using it. It is much more stable than LaTeXML since it forces you to use a stable XML sublanguage and there are validation files baked into an extension available for VSCode. Editing is still not as comfortable as LaTeX since there are no such things like synctex letting you jump to the code generating a specific part of the pdf. And the paragraph tags are quite annoying to be honest.
Manim is a python library geared towards rendering math videos, which are generally not interactive so it probably does not suit you.
Reactive notebooks like Observable (javascript) Pluto.jl (julia) or with more tweaking Jupyter (mostly python, but also R and julia) allow some interactive plots. You could supply these as a supplemental with your paper. But chances are that few people will look into the supplemental much less get them running. Observable is probably you best bet as they are easier to host, so you could provide a link in the paper.
Enhanced Markdown like Quarto (which is based on the older R-Markdown, which only worked for R)
Data Dashboard website makers like Dash by Plotly (python) and R shiny
Perhaps this attempt (typst) at a LaTeX replacement will turn out a better foundation for interactivity in the future (although they do not exist at the time of writing - this is mostly a reminder for my future self)
Conclusion
People are thinking about this problem. But since everyone is time constrained and there is probably very little funding to create tooling there is not much of a toolchain to create such a paper. And without the ability to easily create such papers, there aren't enough papers to fill a journal so I wouldn't expect there to be one (I certainly do not know of one).