Yes, I think that's the general problem. On the printed page (or a digital facsimile of one), footnotes work well because a reader can almost effortlessly redirect their eyes to the bottom of the page and tell at a glance if the footnote is something they care about and want to absorb. Clicking on links, flipping to the bottom of a long page, etc. is far more effort and pretty much defeats the purpose of many types of footnotes.

Again, how the note itself is presented should be definable by the author/publisher, media, device, or user, ranked from least to greatest priority.

Whilst infinite scroll is a misfeature, most such designs are based around subunits, usually articles. Notes at the end of an article, much as they typically appear in printed anthologies, encyclopedias, and collections, would seem a fairly obvious choice.

Most words have more than one meaning - the one you give for footnote is certainly one meaning of footnote, however if I go to https://dictionary.cambridge.org/dictionary/english/footnote it says "a note printed at the bottom of a page that gives extra information about something that has been written on that page" which I actually think is the commonly understood meaning.

This would also explain the strong relation between the words Footer and Footnote.

The Footnote was invented in a particular media, it was presented in a particular way that was suitable to that media. My main point is that there has not been an obvious way to translate between how it is used in that media to how it should be used in the browser, and therefore attempts to make a footnote element specification have met with lackluster response at best.

A footer typically contains information about its section: author, links to related documents, copyright data, etc.

https://www.w3.org/html/wiki/Elements/footer

A <footer> element is one possible container for a <note>. It is not the note itself, need not contain any notes, nor need notes appear in footers.

The mapping is both inaccurate and ambiguous.