refactor(app): give full-screen settings a dedicated route

[Brendonovich]

Summary

• Render full-screen settings at /settings instead of hiding the current route behind a separate surface.
• Remove the settings-specific titlebar guard: settings naturally matches no session or draft tab.
• Keep the selected section and originating server/directory in the URL, including across reloads. Back/Escape returns to the previous page, with Home as the direct-entry fallback.
• Share navigation history between settings, app commands, and native browser/desktop traversal. Section changes replace the current entry; browser reload preserves known history without relying on router location state.
• Preserve the originating directory and selected model when opening a new tab from settings.
• Keep settings open when closing a background tab and recognize settings URLs during desktop restoration.

Stack

Follow-up to #45361. This PR targets settings-tab-focus; merge the focus fix first, then retarget this PR to v2. Includes the latest focus-fix branch and its draft new-tab regression coverage.

Recording

Session -> settings -> Models -> reload retaining remote context -> Back -> Forward -> Back -> settings -> same-tab return. Recorded from 7d19d78601 using the committed mocked regression test, with temporary Playwright slow motion for readability. Viewport and recording: 1280x720; duration: 11.96 seconds. Later history-command and new-tab fixes are covered by the regression tests below.

video.webm

Validation

• App and desktop bun typecheck; app bun run typecheck:e2e
• App unit tests: 543 passed; browser tests: 49 passed, including 4 actual MemoryRouter history tests
• Desktop route-storage tests: 2 passed
• Settings, settings-history, nested-dialog focus, and tab-navigation Playwright regressions: 20 passed
• Coverage includes remote scope, reload, browser and app Back/Forward, same-tab navigation, vertical draft prompt preservation, mobile direct entry, background tab close, and new-tab directory/model preservation
• App production build passed (existing chunk-size/dynamic-import warnings)
• Pre-push workspace typecheck: 32 packages passed