Adds two tests that run the real `ai-gateway start` command against a
real coderd over the production websocket dialer.
`TestAIGatewayStartE2E`: the gateway completes the handshake, loads
providers over DRPC, proxies an OpenAI chat completion on its own
listener, and the interception is recorded in coderd.
`TestAIGatewayStartE2E_InvalidKey`: a key rejected by the handshake is
fatal rather than retried, and the command reports it.
Also tidies the existing tests: `TestAIGatewayStart_HealthBeforeReady`
moves to the external package and reuses the new helpers, the two fake
reloaders collapse into one `mockReloader`.
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Paweł Banaszewski
94f487b890