I just took another look at the mobile app on my Android and missed that there is a little options menu (3 verticals dots) under the "Continue Watching" section while on the Home tab. If you select these 3 little dots, another menu should appear that allows you to view details, watch on mobile, share, and remove from continue watching.
So, apparently, two different ways to continue watching content on your mobile device.
Click on images to enlarge.
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