[3.11] gh-106300: Improve errors testing in test_unittest.test_runner (GH-106737) (GH-108007)

Use a custom exception to prevent unintentional silence of actual errors.
(cherry picked from commit fd9d70a94de5b0756b52b9ae21e236e25545db4f)

Co-authored-by: Nikita Sobolev <mail@sobolevn.me>