chore: Update `openai` example

[dnys1]

• Migrates the OpenAI example to v1
• Updates the prompt generation method to be streaming

[dnys1]

• #200 👈
• #199
• #198
• #197
• #196
• #195
• #193
• main

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Merge activity

• Oct 9, 9:04 AM PDT: A user started a stack merge that includes this pull request via Graphite.
• Oct 9, 9:22 AM PDT: Graphite rebased this pull request as part of a merge.
• Oct 9, 9:22 AM PDT: A user merged this pull request with Graphite.