Add api.responses.write scope to OpenAI OAuth flow

The browser login flow only requested identity scopes, so the resulting
access token lacked permission to call the Responses API.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

lib/crates/arc-openai-oauth/src/lib.rs

@@ -77,7 +77,10 @@ pub fn build_authorize_url(
         ("response_type", "code"),
         ("client_id", client_id),
         ("redirect_uri", redirect_uri),
-        ("scope", "openid profile email offline_access"),
+        (
+            "scope",
+            "openid profile email offline_access api.responses.write",
+        ),
         ("code_challenge", &pkce.challenge),
         ("code_challenge_method", "S256"),
         ("state", state),