feat(libsy-llm-client): report rejected extra_body keys as a configuration error

Problem

Per-target extra_body keys are merged into the outbound request body in
crates/libsy-llm-client/src/client.rs at a point that sits outside the retry loop, so the merge
happens once, before any attempt.

When an upstream rejects the request because of one of those keys — a 400/422 naming an unknown or
unexpected parameter — every retry re-sends the same rejected key. The retry cannot succeed, and
there is no way for a caller to say "drop this knob and try again".

The case we hit in practice: reasoning-control knobs (chat_template_kwargs, enable_thinking) that
some OpenAI-compatible servers accept and others reject outright. A call carrying the knob fails
permanently against a rejecting server, even though the identical call without it would succeed.

Proposal

Move the extra_body merge inside the retry loop and allow named keys to be dropped after a
parameter rejection. Roughly 20 lines.

Deliberately narrow:

• Only a 400/422 whose body names the parameter, or an unknown/extra-parameter condition,
  qualifies. A 429 or 5xx must surface as-is — silently stripping a knob and re-firing on a
  rate limit would double the load and mask the real failure.
• Retry exactly once without the knob. No escalation ladder, no second strip.

Scope

crates/libsy-llm-client/ only. Benefits every route that configures extra_body, which is why it
seems worth doing as its own change rather than inside a feature PR.

Notes

Happy to open the PR. Wanted to check the direction first, since it moves an existing statement
across the retry boundary rather than adding alongside it — if you'd prefer a different shape (e.g.
an explicit per-target "droppable keys" list instead of inferring from the reject), that's easy to
adjust.

Start in crates/libsy-llm-client/src/client.rs, locate the per-target extra_body merge and the retry loop, then trace how upstream 400/422, 429, and 5xx responses are classified. Done means a named-parameter rejection retries exactly once without that key, while rate-limit and server errors are surfaced unchanged; keep the change within crates/libsy-llm-client/.