test/looks.test.ts: the look-while-tests-run case holds the app's tests open with a gate, not a 2 s sleep #1077

Replaces #968, parked twice:

• the check failed ("capacity: only a forge admin reads or changes it > an admin changes each one from the page, the API and MCP; a wrong value is refused; every change is kept") and the decider saw no point in another try (pull #991 closed). Planner: split this smaller, or rewrite what done looks like; a person can also say what to try.
• the check failed ("capacity: only a forge admin reads or changes it > an admin changes each one from the page, the API and MCP; a wrong value is refused; every change is kept") and the decider saw no point in another try (pull #1025 closed).

Those checks went red on tests this change does not touch. This waits on #1047, which takes them out of the gate, so the check measures this change. Start from today's main. What done looks like is #968's, unchanged:

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Pillar: P0 Trust (#586). Split from #842, which was parked twice on other files' flakes.

"a look is taken from app.serving, while the deploy's tests are still running…" (test/looks.test.ts, around line 426) gives the app a test of sleep 2 && exit 1 and assumes the look lands within those 2 s. On a busy runner the check has already failed: Expected: "running", Received: "failed".

Done looks like

• [ ] The app's test blocks on a gate the test releases, such as a file it creates once the look is taken, and then exits 1. Nothing else in the assertion changes.
• [ ] Only test/looks.test.ts changes. It passes 20 times in a row with test/studio.test.ts running alongside. Quote the loop's output.
• [ ] Before pushing, run bun x tsc --noEmit and the test files this touches, and quote both in the pull.

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