How to publish a Mathematica notebook to a journal as supplementary material?

Question

I've done part of a proof via Mathematica. In the appendix of the paper I've linked to this published notebook, since I misunderstood "With any paid subscription plan, all files stored in the Wolfram Cloud never expire.". I just found out that when your subscription ends the published cloud files cannot be accessed anymore, which makes this feature useless for publishing papers. When I publish a mathematical paper I want it to be still accessible in hundreds of years.

So I've tried to save my notebook as pdf or LaTeX, which both gives terrible results. The pdf basically just shows a bunch of random characters instead of the actual content and the LaTeX code gives multiple errors when I try to compile it and it is not able to make proper line breaks, such that the formulas are cut off. HTML works kind of okay-ish in the sense that one can guess the content most of the time since the majorities of symbols are shown kind of correctly (some curly brackets are not shown). Is there any possibility to put a version of a Mathematica notebook into a publication that is readable for everyone without the need of any license. At least something like a screenshot of my monitor (but the notebook does not fit on one notebook as it spans over multiple pages). Am I doing something wrong when I try to save my notebook as pdf (or print it)? I can barely believe that such an expensive software as Mathematics fails so hard in implementing such a basic feature. The save as PostScript is by the ways as buggy as the printing feature as well.

The pdf looks like this: and I don't really see how this is connected to my notebook.

E.g.,if I create the simplest Mathematica notebook I can think of:

The result looks like this:

which is completely useless. If it doesn't work for this simple example, I ask myself the question if there ever was a single case in the history of Mathematica, where the "save to pdf" feature actually gave a kind of useful result?