Continuing pages in Page Layout Document in Pages

In my experience, when you paste a link or write it out, you just need to go on typing and Pages automatically converts it to clickable text.

You can't!

You can't insert a section break in a layout document because layout documents don't have sections; each page it its own section. See Creating Sections:

In a page layout document, each page is one section. You can use the predefined sections as they are, or you can modify or remove them one page at a time.