Expand error status test coverage

- Added explicit status validation across error handling tests.
- Added lifecycle and slot-leak checks to older tests.
- Improved unhandled-error propagation coverage.
- Added repository guidance and a test runner script.
- Verified all 23 CTest tests pass.

Co-Authored by Codex GPT 5.4

tests/err_capture.h

@@ -75,6 +75,12 @@ static int __attribute__((unused)) akerr_slots_in_use(void)
 	}							\
     } while ( 0 )
 
+#define AKERR_CHECK_STATUS(errctx, expected_status)			\
+    do {								\
+	AKERR_CHECK((errctx) != NULL);					\
+	AKERR_CHECK((errctx)->status == (expected_status));		\
+    } while ( 0 )
+
 #define AKERR_CHECK_CONTAINS(needle)				\
     AKERR_CHECK(strstr(akerr_capture_buf, (needle)) != NULL)