The shared proxy wrapper in tests/e2e/e2e_gateway.py was misnamed: Gateway is
not a gateway server, it is the client every suite uses to talk to the proxy
(keys, models, chat/embed/ocr, spend read-backs, poll helpers). Rename the
module to proxy_client.py and the class to ProxyClient, with build_gateway
becoming build_proxy_client and the GatewayProvider protocol becoming
ProxyClientProvider. The .gateway attribute suites held is now .proxy. Only
identifiers changed; prose and string literals that use the word gateway for the
proxy-server concept were left alone.
Each suite previously built its own instance through a per-suite build_client()
that called build_gateway() inside, duplicating the proxy wiring across suites.
There is now one session-scoped proxy fixture in tests/e2e/conftest.py; every
suite's client fixture depends on it and injects it, so the wiring lives in one
place. claude_code keeps building its own client directly since it has its own
harness and does not use the shared fixtures.
Behavior is unchanged: shared transport, data-plane/control-plane split routing,
poll budget, typed request/response models, and resource cleanup all go through
the same object.
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