Fix : make playwright tests idempotent (#13332)

### What problem does this PR solve?

Playwright tests previously depended on cross-file execution order
(`auth -> provider -> dataset -> chat`).
This change makes setup explicit and idempotent via fixtures so tests
can run independently.

- Added/standardized prerequisite fixtures in
`test/playwright/conftest.py`:
- `ensure_auth_context`, `ensure_model_provider_configured`,
`ensure_dataset_ready`, `ensure_chat_ready`
- Made provisioning reusable/idempotent with `RUN_ID`-based resource
naming.
- Synced auth envs (`E2E_ADMIN_EMAIL`, `E2E_ADMIN_PASSWORD`) into seeded
creds.
- Fixed provider cache freshness (`auth_header`/`page` refresh on cache
hit).

Also included minimal stability fixes:
- dataset create stale-element click handling,
- search wait logic for results/empty-state,
- agent create-menu handling,
- agent run-step retry when run UI doesn’t open first click.

### Type of change

- [x] Test fix
- [x] Refactoring

---------

Co-authored-by: Liu An <asiro@qq.com>

test/playwright/helpers/_auth_helpers.py

@@ -30,8 +30,10 @@ def ensure_authed(
     if seeded_user_credentials:
         email, password = seeded_user_credentials
     else:
-        email = os.getenv("SEEDED_USER_EMAIL")
-        password = os.getenv("SEEDED_USER_PASSWORD")
+        email = os.getenv("SEEDED_USER_EMAIL") or os.getenv("E2E_ADMIN_EMAIL")
+        password = os.getenv("SEEDED_USER_PASSWORD") or os.getenv(
+            "E2E_ADMIN_PASSWORD"
+        )
     if not email or not password:
         pytest.skip("SEEDED_USER_EMAIL/SEEDED_USER_PASSWORD not set.")
 
@@ -45,22 +47,16 @@ def ensure_authed(
 
     try:
         if "/login" not in page.url:
-            if (
-                page.locator(
-                    "input[data-testid='auth-email'], [data-testid='auth-email'] input"
-                ).count()
-                == 0
-            ):
-                try:
-                    page.wait_for_function(token_wait_js, timeout=2000)
-                    return
-                except Exception:
-                    pass
+            page.wait_for_function(token_wait_js, timeout=2000)
+            return
     except Exception:
         pass
 
     page.goto(login_url, wait_until="domcontentloaded")
 
+    if "/login" not in page.url:
+        return
+
     form, _ = active_auth_context()
     email_input = form.locator(
         "input[data-testid='auth-email'], [data-testid='auth-email'] input"