Use the conversation tray for mobile navigation

[witbrock]

Mobile and narrow/touch windows now use the shared left conversation tray regardless of the saved desktop layout. Previously these windows forced the horizontal list. The tray can be closed and reopened with a touch-sized control, closes when a conversation is selected, and preserves the current conversation and supported in-memory drafts. Desktop-only layout and hover settings are hidden on mobile.

Native task: #V#task_agent_ffde8f01dd70ea877ea110bcee66ee92.

Existing storage keys and separate mobile/desktop collapse preferences are retained. Fresh mobile profiles start open; existing collapsed profiles retain their choice. Desktop horizontal/vertical preferences are preserved. No preference migration, conversation reordering, unread semantics, import/federation, model routing, database or infrastructure changes.

Validation (Tier 1):

• Candidate 25e81c169f70136f4531c40a78e882efc56b0b2a: 47 focused/integration tests and three targeted layout-menu tests passed, including draft and unified-catalogue coverage. Static lint and diff checks passed; both CI checks passed.
• Seven production-template simulated viewport profiles passed, from 320px phone to desktop. These earlier checks use synthetic content.
• Authenticated localhost AgentTest acceptance uses the exact clean candidate, normal visible fixture login, a dedicated disposable actor/organisation, and two actual saved conversations. Fresh and existing horizontal/collapsed mobile preferences, selection, close/reopen, Escape/focus, hover isolation, orientation, per-conversation drafts, refresh selection, mobile settings and desktop navigation were exercised. No API/admission mocking or model requests.
• Evidence and screenshots are retained at .run/mobile-tray-evidence/authenticated-20260917/ in the controller-owned worktree. Earlier test receipts are in .run/mobile-tray-evidence/resumed-20260917/.

Merge decision changes — ready: authenticated acceptance resolves the remaining gate; no candidate-caused loss of navigation, supported drafts/selection, or usable chat width was observed. Current main's additional execution-timing/receipt work does not change the affected frontend path.

Limitations: Chromium viewport/touch emulation is not physical-device/PWA or public OAuth acceptance. Drafts remain in tab memory and are not automatically restored after page reload, matching the documented baseline. Earlier broad clipboard and keyboard-sized composer/footer failures reproduced on unchanged baseline and remain outside this tray repair. No public deployment is requested or performed, and this PR does not claim the public defect has already been fixed.