[FR] `--json`: Save metadata as JSON

I like to track usage costs. Previously, I manually counted the tokens in the inputs and outputs. However, now that models support multimedia input/output, reasoning tokens, and more, my previous approach is no longer feasible. It would be helpful to provide a --json (e.g., --log-json, --json-out, etc.) option that saves the input/output token count and other metadata to a JSON file. This way, my wrapper can read the exact token usage and compute the costs accordingly.

Including the inputs and outputs in this file would also make it useful for logging. In general, this file offers a way to output information without cluttering stdout and hindering interactive, streaming usage.

Start by locating the command-line option handling and the paths that produce token counts, model metadata, inputs, and outputs. Define the JSON file's contents and how it avoids cluttering stdout, then verify that a wrapper can read exact usage and logging data without disrupting interactive streaming.