test(e2e): stabilize chat token refresh spec

e2e/specs/mock/chat/chat-send-token-refresh-retry.spec.ts

@@ -3,7 +3,8 @@ import { expect, test, type Request } from "@playwright/test";
 import { mockCoreApis } from "@e2e/fixtures/api-mocks";
 import {
   clearBrowserState,
-  signInWithEmailAndOpenChat,
+  enterChatFromSplash,
+  setEmailSessionStorage,
 } from "@e2e/fixtures/test-helpers";
 
 test.beforeEach(async ({ baseURL, context, page }) => {
@@ -23,7 +24,8 @@ test("chat send refreshes an expired token, retries the request, and renders the
     }
   });
 
-  await signInWithEmailAndOpenChat(page);
+  await enterChatFromSplash(page);
+  await setEmailSessionStorage(page);
 
   const message = "token refresh retry test";
   const messageInput = page.getByRole("textbox", { name: "Message" });