#24944 cmux NEXT composer: keep Codex look dots inside the composer

Leo's third composer ask (2026-10-24):

"especially for the bottom bits, the bottom dots, like I said, you know, when it's in the codex mode, just put it at the bottom of the dead space inside the composer, not, like, at the bottom. Like I already said this. I'm pretty sure we already made pull requests for this, but it's just, like, nothing happened, really."

The merged #24395 behavior rendered Codex look dots as a sibling band below the composer box. This PR moves the dots and their label into a 16px internal dead-space row in the Codex composer box, keeps the parent bottom gutter closed, and asserts the row stays inside the box bounds. Claude's quiet-row placement and dot keyboard/focus behavior stay unchanged.

Gallery before/after (base feat-cmux-next vs this head): Codex dots gallery compare

Earlier-attempt reconciliation: merged #24395 introduced the outside band; open #24519 is a live-owner broader look-layout follow-up and is not adopted. This corrective PR is limited to the Codex chat dots' container and regression assertion.

Validation:

• bun run typecheck (webviews): pass.
• Composer row unit tests: 4 pass; browser dots suite is wired but skipped locally because the browser lane is unavailable under host pressure.
• Targeted vp fmt --check: pass; git diff --check: pass.

Agent session: big-red

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