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The majority of announcement bars utilize a horizontal slider script. The simplest method is to swap it out for a vertical slider. Wrap each message in a stacked container, set the wrapper to overflow hidden with a fixed height, and animate the inner container with transform translateY at a timed interval. This makes for smooth vertical autoplay and endless looping.
Your announcement bar moves sideways because of how its animation is coded. To make it slide up and down, you need to change the movement direction to vertical and set a fixed height on the container so it hides the other messages until they slide into view.
If your theme uses a built in slider script like Flickity, it usually has a quick vertical setting that handles both the direction and the auto looping for you, meaning your current auto play timing will keep working perfectly.