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/auth_test.rs

@@ -8,9 +8,8 @@ use common::{TestConfig, test_user};
 
 #[tokio::test]
 async fn valid_api_key_returns_user() {
-    let app = doctate_server::create_router(
-        TestConfig::new().with_user(test_user("dr_test")).build(),
-    );
+    let app =
+        doctate_server::create_router(TestConfig::new().with_user(test_user("dr_test")).build());
 
     let response = app
         .oneshot(
@@ -32,9 +31,8 @@ async fn valid_api_key_returns_user() {
 
 #[tokio::test]
 async fn invalid_api_key_returns_401() {
-    let app = doctate_server::create_router(
-        TestConfig::new().with_user(test_user("dr_test")).build(),
-    );
+    let app =
+        doctate_server::create_router(TestConfig::new().with_user(test_user("dr_test")).build());
 
     let response = app
         .oneshot(
@@ -52,9 +50,8 @@ async fn invalid_api_key_returns_401() {
 
 #[tokio::test]
 async fn missing_api_key_returns_401() {
-    let app = doctate_server::create_router(
-        TestConfig::new().with_user(test_user("dr_test")).build(),
-    );
+    let app =
+        doctate_server::create_router(TestConfig::new().with_user(test_user("dr_test")).build());
 
     let response = app
         .oneshot(