Tiny fixes

• Ensure the websocket context is present in websocket subtasks.
• Increase httpx pool limits twentyfold to avoid pool clogging.
  Since we’re currently pooling connections in a single client, 100 connections is a too low a limit given the number of connections we need to handle.
  In future, we should probably reduce the reliance on a single client and only reuse a global client in some cases but not in the others.