Ensuring user knows scrolling is an option

Adding a truncation ellipsis to the last word is risky, because the user might think that the “Next” button will provide more content.

The problem you’re describing is called a false floor or illusion of completeness issue. A common solution is to make sure that the design deliberately looks incomplete. We see this on carousels that show just a little bit of the off-screen item (image is from the linked article):

Old Netflix carousel showing peeking offscreen items

You could make the bottom-most line of the visible content peek out, instead of looking like something complete. If that’s too subtle, your idea of a custom scrollbar could work. It could always be showing, and act as a deliberate signifier that there’s an interaction that the user needs to do.

If it’s mandatory or highly necessary that the user read all of the content on each screen, you might also disable the Next button until the user scrolls to the bottom to ensure that they don’t accidentally skip.