Remove OPENAI_API_KEY from recorded (playback) test steps

[Copilot]

• Remove OPENAI_API_KEY env var from "Run recorded tests" step in .github/workflows/live-test.yml
• Remove OPENAI_API_KEY env var from "Run recorded tests" step in .github/workflows/release.yml
• Fix ResponsesTests.cs: replace 3 TestEnvironment.GetTestClient<ResponsesClient> calls with GetProxiedOpenAIClient<ResponsesClient>
• Fix ResponsesToolTests.cs: replace 4 TestEnvironment.GetTestClient<ResponsesClient> calls with GetProxiedOpenAIClient<ResponsesClient>

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[joseharriaga]

@copilot Looking at the workflow runs for this PR, it looks like several of the Responses tests failed. They all have the same error in common: "Incorrect API key provided". Based on this error, it sounds like the tests were attempted to run in live mode rather than in playback mode, and because there is not API key available, the live service returned an error which makes sense. We must fix these tests to run fully in playback mode. By the looks of it, the problem is that these tests are calling TestEnvironment.GetTestClient<ResponsesClient> instead of GetProxiedOpenAIClient<ResponsesClient>, which means that they are skipping the recording framework instrumentation entirely. Please fix these tests accordingly.

[Copilot]

@copilot Looking at the workflow runs for this PR, it looks like several of the Responses tests failed. They all have the same error in common: "Incorrect API key provided". Based on this error, it so...

Fixed in 6bacd1f. Replaced all 7 TestEnvironment.GetTestClient<ResponsesClient> calls with GetProxiedOpenAIClient<ResponsesClient> — 3 in ResponsesTests.cs and 4 in ResponsesToolTests.cs.