How do I get rid of a split screen in Messages?

Perhaps you refer to the Message list - seen to the left of the main conversation pane. When your iPad is being used in Landscape orientation, the Message list will always be visible - and cannot be suppressed.

Apple invite submission of comments and feature requests via its Product Feedback portal. If you would like to see the ability to hide the message list in a future version of iPadOS, this would be the most appropriate channel to direct a request:

Feedback - iPad - Apple