Remarkable

No, if you are in a PDF file, dragging the page will just give you blank space below the PDF.

If you hack the device and add a custom template, I don't know what happens, but I doubt it will create a new page with the template. I suspect you will need to use the add page feature (which will copy the underlying template to the new page), or use an rM template that supports infinite scroll (lines or dots).

So there isn’t a shorthand gesture that does that but the tablet does have that functionality.

You can click to see an overview of the pages and can duplicate a page at will (it just doesn’t have a shorthand gesture without a hack or custom templates as far as I know).

So it won’t do it in response to a quick swipe but it can duplicate pdf pages infinitely

Templates are image files which are used as "background images" for pages in notebooks, i.e. documents which are not PDF files. In a notebook, you can choose which template you want to use for every page, including using the same template for multiple pages. The reMarkable software comes with a collection of templates.

PDF files can be duplicated, but individual pages within a PDF file cannot. Pages within a PDF can be re-ordered, and blank pages can be inserted into the document. When you're viewing a PDF file, the original page from the PDF is the "background image" for that page. (The same is true of EPUB files, which are converted to PDF when you upload them to the tablet.)

Custom templates are not supported by reMarkable (the company), but there are ways to upload new templates to the tablet and "trick" the reMarkable software into using them. This page (which I really need to update) has more detail about this.

If you want to upload custom templates but you're not comfortable with using SSH and editing JSON files, you'll probably want to look into a third-party solution. RCU is what I use, it's not free but it's not expensive, and it does a lot more than just custom templates.