feat(ui): one consistent navbar on every page (TODO.md L3)

tests/e2e/test_admin_auth.py

@@ -101,9 +101,11 @@ def test_anonymous_chat_without_tuning(
 
     # Header: Sign in offered, Sign out not.
     expect(page.locator("#sign-in-link")).to_be_visible()
-    expect(page.locator("#sign-in-link")).to_have_attribute(
-        "href", "/login.html?next=/sources.html"
-    )
+    # Phase 34 task 02: the shared header module rewrites the static
+    # ?next= fallback to the CURRENT pathname ("return to where you
+    # were") — on the chat page that is "/" (the markup keeps
+    # ?next=/sources.html as the no-JS fallback only).
+    expect(page.locator("#sign-in-link")).to_have_attribute("href", "/login.html?next=/")
     expect(page.locator("#sign-out-btn")).to_be_hidden()
 
     # Chat still streams a grounded answer (with source chips) for