fix: Don't log internal exception for tornado user auth (#5208)

#### Issues

* resolves: #5194
* resolves: PY-2004

Author: sl0thentr0py

sentry_sdk/integrations/tornado.py

@@ -176,8 +176,13 @@ def tornado_processor(event, hint):
             request_info["env"] = {"REMOTE_ADDR": request.remote_ip}
             request_info["headers"] = _filter_headers(dict(request.headers))
 
-        with capture_internal_exceptions():
-            if handler.current_user and should_send_default_pii():
+        if should_send_default_pii():
+            try:
+                current_user = handler.current_user
+            except Exception:
+                current_user = None
+
+            if current_user:
                 event.setdefault("user", {}).setdefault("is_authenticated", True)
 
         return event