Ensure multi-client configurations use new ProxyClient (#1045)

Add structured content & update almost all tests

Add "http" as an alias for streamable-http

Update docs and test

Update tests

Simplify code for running servers in processes

Update test typing

Update test_openapi.py

Ensure behavior-affecting headers are excluded

Ensure content-length is always stripped from client headers

Update tests for new names

Use lowercase name for headers

Update test_openapi.py

Ensure headers are passed through proxy servers

Pass client headers through to OpenAPI client