Add complete multi-round Messages usage accounting

Problem statement / motivation

Operators need the full inference cost of a Messages turn, including rounds used by built-in tools. Provide consistent, documented accounting for JSON and SSE clients without counting repeated usage snapshots more than once.

Proposed solution

• Add a typed per-round usage accumulator and a turn aggregate shared by the JSON and streaming Messages paths.
• Define input, output, cache-read, and cache-creation accounting for supported upstream fields. Distinguish missing usage from zero and retain documented provider semantics.
• Specify how complete turn usage is exposed while preserving the native Messages streaming schema. If the wire protocol cannot represent every total, document a separate typed telemetry surface rather than inventing wire fields.
• Separate per-round records from the aggregate so downstream metering counts each inference contribution once.

Acceptance criteria

• Deterministic one-, two-, and multi-tool-round fixtures verify totals for JSON and SSE.
• Tests cover initial/terminal usage snapshots, repeated cumulative counters, absent/partial usage, cache counters, and unknown supported extensions.
• JSON and SSE expose equivalent complete-turn accounting through the documented surfaces.
• Errors, cancellation, client-tool handoff, and round-limit exhaustion report available usage as partial when appropriate; they never fabricate a completed total.
• Usage from hidden built-in-tool rounds is included without exposing their internal content or double-counting the public aggregate.
• Document units, accounting boundaries, and examples for operators.

Additional context

Enterprise Readiness enhancement. Coordinate with #279 for OpenTelemetry export; this issue owns usage semantics and correctness, not a billing platform.

Source review at afa6c14, not a new runtime reproduction: Messages streaming and Messages JSON loop.

Enterprise Readiness tracker: https://github.com/vllm-project/agentic-api/issues/316

Start with the referenced messages_stream.rs and messages_loop.rs at commit afa6c14, then trace how JSON and SSE paths represent usage across inference rounds. Add deterministic one-, two-, and multi-tool-round fixtures covering the listed usage cases, and document the accounting units, boundaries, and exposure surfaces. Done means JSON and SSE provide equivalent complete-turn accounting without double-counting, while partial outcomes remain marked partial.