Thank you for your feedback.
You can archive your message threads in Messages app by long-pressing on a thread. When you long-press a thread, a menu will display on the top-right with a few icons. You can tap on the file icon with a downward arrow. You can access archived messages by tapping on the "More" menu (Hamburger button) then "Archive".
We hope this resolves your concern. If not, please reply to this post.
We appreciate your contribution to the Beta Program.
One UI Beta Team