I have the same problem with you. When I press the messages tab in my profile nothing happens. The links are just like yours but they stop to members page/my page/messages/compose. This happens with every messages tab, and just like you, I have an empty page below that nav menu.
I am developing my own theme, but I have tested it with 3 different twenty themes and I have the same issue with the messages tab. All the other links are working except for messages.
I hope we get a solution with this.
If I find anything sooner, I will post again with my solution.
*I am using local by flywheel for the development
