canary(auth-live-canary): widen chat-wait deadlines 120s -> 300s

The auth-browser-consent google probe completed OAuth + extension
activation successfully on CI but timed out at the next step
(send_chat_and_wait_for_terminal_message), with the agent stuck on
"Thinking (step 1)" for the full 120s budget. Local runs on the
same code path complete the chat in ~36s, but ubuntu-latest 2-vCPU
runners under cold-start load (gateway restart, mock LLM bootstrap,
WASM tool first-invocation) need substantially more headroom.

300s matches the precedent set by `d8765714 ci(canary): revert
auth-smoke to ubuntu-latest + widen budgets to 300s/360s` for the
auth-smoke lane on the same runner class.

Both call sites widened — the seeded Responses-API probe at line 221
and the browser_oauth probe at line 800.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

scripts/auth_live_canary/run_live_canary.py

@@ -218,7 +218,7 @@ async def seeded_browser_probe(
         result = await send_chat_and_wait_for_terminal_message_fn(
             page,
             probe.response_prompt,
-            timeout=120000,
+            timeout=300000,
         )
         thread_id = await page.evaluate("currentThreadId")
         history = await api_request(
@@ -797,7 +797,7 @@ async def browser_oauth_probe(
         chat_result = await send_chat_and_wait_for_terminal_message_fn(
             page,
             case.trigger_prompt,
-            timeout=120000,
+            timeout=300000,
         )
         history_thread_id = await page.evaluate("() => currentThreadId")
         history = await api_request(