refactor(tests): migrate remaining batches to tests/common/

Finishes the lift of shared helpers into `tests/common/`. Covered:
- health, web, oneliners_api, upload (31 tests; upload exercises the
  new `multipart_upload_body` helper driven by doctate_common field
  constants)
- sse_integration, sse_cleanup, transcribe, oneliner_heal_decoupled,
  silent_case_empty, failed_only_case_empty_oneliner,
  transient_failure_retries (24 tests)

Also applied cargo fmt across the test tree and fixed one clippy
needless_borrows_for_generic_args warning in analyze_test.

All 387 tests pass; 3 ignored (as before).

Side effect: health_test previously used a hardcoded `/tmp/doctate-test`
data path, which parallel `cargo test` runs could collide on. The
migration replaces it with the common unique-tmpdir pattern, removing
a latent flake.

server/tests/common/seed.rs

@@ -40,11 +40,7 @@ pub fn seed_recording(case_dir: &Path, stem: &str, transcript: Option<&str>) ->
 /// Like [`seed_recording`] but additionally writes the `.duration.txt`
 /// sidecar — used by the delete-recording tests that assert every
 /// sidecar is cleaned up.
-pub fn seed_recording_with_sidecars(
-    case_dir: &Path,
-    stem: &str,
-    transcript: &str,
-) -> String {
+pub fn seed_recording_with_sidecars(case_dir: &Path, stem: &str, transcript: &str) -> String {
     let filename = seed_recording(case_dir, stem, Some(transcript));
     std::fs::write(case_dir.join(format!("{stem}.duration.txt")), "42").unwrap();
     filename