Headers and footers are print-oriented, but losing footnotes is not ok. They could have displayed on the side, or highlighted in some way to display on mouse over or click. Whatever, just make them available...
I've used the new pageless style for a while and losing footnotes was a little annoying at first, be we adapted. I don't have a perfect solution to it, there are alternatives you can do (glossary or something at the end, with a bookmark on each item, so you can link directly to it).
If you make heavy use of footnotes, don't use the new feature (as others have said). It's a tradeoff, and I mostly prefer pageless, especially when embedding images that are larger (width wise).
I would look at them as sort of a content enrichment. Like a comment applied to the text.
Pageless has comments. Why would it be so bad to place footnotes alongside with comments? Or perhaps on the left side, below the headings index?
I'd even go as far as say Headers and Footers should be preserved but just included once at the very top and very bottom. Unless you toggle back to page mode and then everything just works. No data loss.
Seems like an easy improvement to make to pageless mode in the short term.
https://edwardtufte.github.io/tufte-css/#:~:text=Sidenotes%3...
But I don't think this should stop us from discussing a way to possibly improving a product.