Support sending OpenTelemetry logs over OTLP (http/protobuf)

[mcculls]

Additional Notes

Builds on top of #11250

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Jira ticket: [PROJ-IDENT]

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[chatgpt-codex-connector]

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[dougqh]

Overall, it looks good to me.

I've added a few performance suggestions both my own and from Claude.
I don't feel strongly that any of them must be addressed before this is merged.