You're correct. When "jumping" to a page as a link, the mobile devices sees it as only a page.
My students all have iPad, and when I design with buttons from my home page, I direct them to the top of a module so the forward/backwards buttons are always available. If there is a distinct series that needs to be completed, I add module requirements. In Canvas Student, students also see little green indicators that they've completed/viewed the item. It helps a lot as they monitor their progress.
How do I add requirements to a module?
How do I view Modules in the Student app on my iOS device?
While it is not a solution that will get you the parallel experience as a browser, I hope it's helpful!
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