When you suggest that you converted a Pages document to EPUB with an online converter, it better have been Pages for iCloud converting a Pages document to EPUB, and not some other cloud-based converter.
Apple's Pages adds certain Apple-specific styling within the EPUB that accomodates the Book application and its submission to the Apple Book store. Apple does not guarantee that a Pages generated EPUB will also be compatible with other EPUB readers than Books. Content for Amazon's Kindle should be created in the Kindle book generator from Word or PDF sources. Older Amazon documentation suggests Pages, but I would not trust that now. Yes, EPUB is a standard that is slightly altered by each EPUB generating entity.
Take the same Pages source document and using Pages on Big Sur, open and export that EPUB with embedded fonts and the Layout best for your content. Save it on the Desktop and double-click to add to, and then open in Apple Books. Does that work satisfactorily?
I am unaware of issues in macOS Big Sur that would impact EPUB generation from Pages, provided you had the last version of Pages that is compatible for Big Sur 11.7.10.