CI runs biome with --write, so a formatting regression can never fail the Static checks job

## Summary

The root `check` script — which the CI **Static checks** job runs as `npm run check` — invokes Biome with `--write`:

```json
"check": "biome check --write --error-on-warnings . && ..."
```

In CI, `--write` **reformats the offending files inside the runner and exits 0**. The rewrite is never committed, so the drift stays in the repository while the job reports success. A formatting regression therefore cannot fail CI.

## Measured

Against `origin/main`'s copy of `packages/ai/test/gpt-6-astra-context-window.test.ts`:

| invocation | result |
|---|---|
| `biome check --error-on-warnings .` (no `--write`) | **rc=1** — reports the violation |
| `biome check --write --error-on-warnings .` (the CI form) | **rc=0**, and rewrites the file (4 insertions / 1 deletion) |

So that file is genuinely unformatted on `main` today, and CI has been green on it throughout.

## Why this matters

This is a gate that cannot fail. Its purpose is to reject unformatted code; instead it silently repairs a copy that is thrown away when the runner exits. Two consequences:

1. **Formatting drift accumulates in the repo unnoticed** — nothing ever reports it.
2. **Local and CI disagree.** A contributor running the documented `npm run check` locally gets their working tree rewritten (convenient), while a contributor running `biome check` without `--write` sees a failure CI never shows. That mismatch cost a session real time today: a lane observed the local failure, reasonably inferred it was the cause of a red CI aggregate, and reported it as such — it was not, because the CI form cannot fail that way.

## Suggested direction

Separate the two intentions rather than overloading one script:

- CI should run a **verify** form with no `--write` (e.g. `biome check --error-on-warnings .`), so drift fails the job.
- Keep a **fix** form (`--write`) as a separate script for local use, e.g. `check:fix`.

Whatever the split, the CI path must be able to fail on unformatted input — otherwise the check is decorative.

## Note

The immediate drift in `gpt-6-astra-context-window.test.ts` is being reformatted separately as hygiene. That does not address this issue: the next unformatted file will be equally invisible.

Inspect the root check script and the Static checks job, then run the Biome commands against packages/ai/test/gpt-6-astra-context-window.test.ts to confirm their differing exit codes. Done means the CI path verifies without --write and fails on unformatted input, while any rewriting remains in a separate local-use script.

Written by the indexing model from the issue text.