You can solve this issue. Textra only closes when you directly reply using a notification. By default Textra opens a "Quick Reply with Keyboard" - this method produces a floating reply window that disappears when your message is sent.
To fix this. Open Textra, open Settings, choose Customize Notifications. At the top of this settings page is Action - press the action below (it will either say "Quick Reply with Keyboard" or "Quick Reply no Keyboard"). Change this option to "Full App" - from now on clicking a Textra notification will directly open the full application and it hitting send on a message will return you to either the message thread you replied to or the full list of all ongoing messages.