Issue for this PR

Closes #47514

Type of change

• Bug fix
• New feature
• Refactor / code improvement
• Documentation

What does this PR do?

The active-session composer is recreated when selecting a session tab, but unlike the new-session composer it never restored focus. Restore focus once the destination draft is ready, using the existing saved-caret behavior. Skip blocked/read-only composers and active dialogs; request dismissal and cursor edits do not retrigger autofocus.

How did you verify your code works?

• Reproduced the original failure: the destination prompt was editable but unfocused after the numbered shortcut.
• Four regression cases cover Command and Control mappings, horizontal/vertical tabs, empty and long drafts, start/end caret restoration, repeated switches, and an 800px window. Command mapping is emulated in Linux Chromium, not a native macOS run.
• Existing request-dock tests pass; 90 composer unit tests pass.
• App and E2E typechecks, scoped Oxlint, Prettier, and git diff --check pass.
• The broader browser run passed 8/9 tests. The existing command-registration.spec.ts file-opening test also fails on the unchanged base (4/10 serial runs, including the same missing file-tab assertion), so that failure is outside this patch.
• Production benchmark baseline recorded before the change: 79/100 runs completed; 21 timed out. The warm/review-closed comparison completed 20/20 before and 16/20 after; the four after failures occur during initial fixture readiness, before the measured switch. Among completed runs, first-correct median/p95 changed from 61.95/76.40ms to 80.00/196.90ms; stable median/p95 changed from 145.10/162.80ms to 196.40/449.40ms.
• A fresh unchanged-base comparison completed 18/20, reproducing initial markdown-readiness failures; its first-correct median/p95 was 66.35/88.40ms and stable median/p95 was 151.10/221.10ms. Fixture failures therefore also exist without this patch, but completed after-change timings remain higher. Performance parity is not established; these runs do not isolate the latency difference's cause. All benchmark runs were serial production builds with no retries.

Base: 7a4ad68af6577c5448a8395b0b95e24ceb623faf; tested head: 71ff13133df3a0fa348972f17cbaace79b966a47.

Screenshots / recordings

Real-app narrow-window screenshot (team Slack). Playwright also attaches refocused-composer screenshots to each regression result. Native GitHub attachment upload was unavailable because Browser Control timed out before creating a page.

Checklist

• I have tested my changes locally
• I have not included unrelated changes in this PR

Requested by: @R44VC0RP (vogel via Slack)