I guess I was facing the same issue.

This answer https://stackoverflow.com/a/49496309 shows that you can change the timeout of WebTestClient via annotation (e.g.: @AutoConfigureWebTestClient(timeout = "P1D")).
Check the syntax for Duration.parse(CharSequence text) for the valid values of the timeout String.

The thing is that when we mutate the graphql tester the underlining WebTestClient timeout is not affected. Combining the mutation with the annotation fixed it for me.