fix(web-search): stop inactivity timer after terminal

[yansigit]

Summary

• Stop the web-search response-byte inactivity timer after an adapter emits a terminal event.
• Keep the distinct post-terminal drain timeout responsible for bounded iterator cleanup.
• Make the regression deterministic by draining longer than the pre-terminal inactivity window.

Verification

• bun test tests/web-search/web-search-progress-stream.test.ts (21 pass)
• bun run typecheck
• bun run test:changed (20,610 pass, 17 skip, 0 fail)
• Independent code review: approved with no concerns.
• Production config SHA-256, mtime, mode, and invalid/backup inventory remained unchanged before and after tests.

Checklist

• Scope stays focused and avoids unrelated cleanup.
• Added/updated tests for behavior changes under src/ or gui/src/, or obtained test-exception-approved (check: bun run check:hygiene).
• Docs or release notes were updated when needed.
• Security-sensitive changes were reviewed for secrets, auth, and unsafe defaults.

No documentation update is needed because this fixes internal timeout ownership without changing configuration or public behavior.

[github-actions]

✅ Deterministic PR hygiene checks passed.

[github-actions]

PR automation (bot-owned)

• Class: same-repo-human (same-repo-human)
• Base: e00690fea4730f1aa6234b1d81ef11dbaf27361c
• Head: ad17cfd708afd3ff326cd81ad7432a05163025cf
• Action: observed
• Exact-head gate: PASS
• Sensitive paths: none
• Maintainer auto-merge approval: NO
• Bot merge evidence: NO
• Next action: wait for exact-head checks