Spring has 2 setups for the MockMvc:
In general what kind of testing is MockMvc used for?
I would say that both methods are for integration testing, but standalone force you to specify which controller you are testing.
WebApplicationContext setup is loading whole context, so you don't care where is specific controller which serves for example /people
POST requests.
So I would recommend using WebApplicationContext setup for testing your REST API in terms of interface which application need to work with. You dont couple test with actual code then + you are documenting the way the app should behave.