show sync button for admin

tests/e2e/test_chat_persistence.py

@@ -272,13 +272,13 @@ def test_persists_across_page_navigation(
     _ask_deflected(page, OFF_TOPIC)  # mixed conversation: grounded + deflected
 
     # A trip to Sources (phase 16: the catalog is admin-only — the trip
-    # starts with a real form login). Phase 19 (owner permission
-    # 2026-08-23): the New chat control is part of the SHARED bar, so it
-    # is present on the sources page too — only clicking it would clear
-    # the conversation (pinned in tests/e2e/test_shared_header.py).
+    # starts with a real form login). The New chat button is chat-page
+    # only (owner rework 2026-08-28 — it left the shared bar), so the
+    # sources page carries none of it (pinned in
+    # tests/e2e/test_shared_header.py).
     login(page, app_url, next="/sources.html")
     expect(page.locator("#docs-tbody tr").first).to_be_visible(timeout=15_000)
-    expect(page.locator("#new-chat-btn")).to_be_visible()
+    expect(page.locator("#new-chat-btn")).to_have_count(0)
 
     # Back to the chat: the conversation is exactly as left — both turns,
     # the source chip, and the amber deflected bubble with its chips.