fix(app): focus session search when the Home shortcut opens Home

[opencode-agent]

Problem

Pressing the Home shortcut (Cmd+B, or Alt+Home on Windows) from a session opens Home, but nothing takes focus. The previously focused composer unmounts, focus falls back to the document body, and typing does nothing. Cmd+F was the only way to reach Search sessions.

Change

• The home.toggle command records a one-shot request in the layout context when it navigates to Home.
• The Home session search controller consumes that request on mount and focuses the search input, so typing filters sessions immediately.
• Clicking or tapping the Home button and titlebar back/forward do not request focus, so pointer and mobile behavior are unchanged (no on-screen keyboard popping up). Pressing the shortcut again still returns to the previous tab, because modified keybinds fire from inside the input.

Testing

• New case in the Home keeper suite (e2e/regression/home.spec.ts): from a session with the composer focused, Cmd/Ctrl+B focuses session search, typing filters to the matching session, the shortcut returns to the session, and clicking the Home button leaves the search unfocused. Verified it fails on v2 without the fix (search not focused).
• home.spec.ts, settings-search.spec.ts, and tabs.spec.ts pass locally (chromium).
• bun run typecheck in packages/app passes; Prettier is clean.

Requested by: @Brendonovich (Brendan via Slack)