The following is only about whether the footnotes display in a separate window in the Calibre viewer, as I have realised, and not the "continuation " issue.
Some time ago I took a decision that where possible I would, when constructing an ebook, have notes as footnotes (i.e. they would be at the end of the chapter which referred to them) rather than endnotes (all consolidated in a single file at the end of the book). The reason for this was that I mainly viewed books on the Bebook 1, a slow device and I reasoned that it would take less processing to skip between locations in the same file rather than having to open another file and then go back to the first one.
Most of the books I have built in this way are done in LibreOffice and then exported using the writer2epub add-on (IIRC roger64 uses or used this export mechanism), and the links it builds have the id of the footnote not included in the <p> tag.
The result seems to be that on any books I have built this way I have never even seen the "footnote" window which as far as I can see is only triggered when the footnotes themselves are in a different file from the referring link. (The book I provided the extracts from was a modified Gutenberg one so didn't follow that principle)
Having looked at displays in other readers including Adobe, in general they seem to display notes in the same window, although I think ALreader does have an option to display footnotes at the bottom of the page containing the reference, though I haven't had much experience with ALreader only just having acquired an Android ereader.
Designing a book with a particular viewer's idiosyncrasies in mind strikes me as a sure recipe for problems, however if the book is just for your own consumption then your rules apply.
BobC