Generally Test plan creation is limited to users subscribed to Test Manager extension or VS/MSDN subscribers.
Basic license users can only run tests. You need a valid Visual Studio
subscription (Enterprise, Test Professional or MSDN Platforms) or Test
Manager license ($52 monthly):
https://marketplace.visualstudio.com/items?itemName=ms.vss-testmanager-web
to create test plans.
See this thread : Can't add a new test plan
So please check if you have the license to create the test plan, and for an paid extension you must assign that extension to users who need access, so they can start using that extension's capabilities. Please see Assign paid extension access to users
Whatever, I can reproduce the issue on myside, seems it's an issue with the preview feature.
As a workaround you can create the Test Plan with MTM (Microsoft Test Manager) or REST API (Test Plans - Create). Both work for me, but the test plan will not display immediately after creating it, you may need to wait for several minutes to sync it.