[BUG] Update to async'ified, limited client.

[rescrv]

The client would open an unbounded number of connections. Bound it so
that they will only open so many connections at once.

[github-actions]

Reviewer Checklist

Please leverage this checklist to ensure your code review is thorough before approving

Testing, Bugs, Errors, Logs, Documentation

• Can you think of any use case in which the code does not behave as intended? Have they been tested?
• Can you think of any inputs or external events that could break the code? Is user input validated and safe? Have they been tested?
• If appropriate, are there adequate property based tests?
• If appropriate, are there adequate unit tests?
• Should any logging, debugging, tracing information be added or removed?
• Are error messages user-friendly?
• Have all documentation changes needed been made?
• Have all non-obvious changes been commented?

System Compatibility

• Are there any potential impacts on other parts of the system or backward compatibility?
• Does this change intersect with any items on our roadmap, and if so, is there a plan for fitting them together?

Quality

• Is this code of a unexpectedly high quality (Readability, Modularity, Intuitiveness)