Add integration test for Fork Project Form Submission

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The following discussion from !53544 (merged) should be addressed:

• @vitallium started a discussion: (+1 comment)

  suggestion (non-blocking): Since these tests validate the behavior do you think we can move them to feature tests too? I am fine with leaving them here but IMO they look like integration tests.

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Please also see comment to test "Actual Forking" use case > !55461 (comment 520726904)