Implement transparent client pattern and middleware error handling #137
Description
Not in scope for this PR, as it would make it too large and this can focus on introducing the client into the existing module, but we should follow a transparent pattern for using the client [as was done for Python](https://github.com/seamapi/python/blob/cb26ee4f9544fafae3e3614f1b02eda41a3445a6/seam/routes/access_codes_simulate.py#L23-L27) and move error handling into middleware.
Originally posted by @razor-x in #134 (comment)