[3.12] gh-106300: Improve errors testing in test_unittest.test_runner (GH-106737) (#108006)

gh-106300: Improve errors testing in test_unittest.test_runner (GH-106737)

Use a custom exception to prevent unintentional silence of actual errors.
(cherry picked from commit fd9d70a)

Co-authored-by: Nikita Sobolev <[email protected]>

Author: miss-islington