The main motivator behind this PR is that `stream_chat_completions()`
was not adding the `"tools"` entry to the payload posted to the
`/chat/completions` endpoint. This (1) refactors the existing logic to
build up the `"tools"` JSON from `client.rs` into `openai_tools.rs`, and
(2) updates the use of responses API (`client.rs`) and chat completions
API (`chat_completions.rs`) to both use it.
Note this PR alone is not sufficient to get tool calling from chat
completions working: that is done in
https://github.com/openai/codex/pull/1167.
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[//]: # (BEGIN SAPLING FOOTER)
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* #1167
* __->__ #1177
