fix(app): clear active tab while settings is open

[Brendonovich]

Summary

• Clear the active session/draft tab while full-screen settings is open, for both horizontal and vertical tabs.
• Keep tab memory unchanged and let clicking the underlying tab return to the app.
• Add regression coverage for opening settings, returning to the app, and selecting the same tab.

Before / After

Settings open over the deterministic remote session from packages/app/e2e/regression/remote-session-settings.spec.ts. Before: fedf017e25 (v2 at capture). After: fdd8abc9df. Identical Chromium, dark theme, fixture data, route, and viewport within each pair. The session tab is no longer highlighted while settings is open.

Layout	Before	After
Horizontal, 1280x720
Vertical, 1280x720
Mobile, 390x844

Vertical and mobile captures set settings.v3.appearance.tabLayout to vertical; mobile correctly uses the horizontal fallback. The dev-only badge is hidden for captures. These images cover fdd8abc9df, not later follow-up commits.

Validation

• bun typecheck in packages/app
• PLAYWRIGHT_PORT=4573 bun run test:e2e e2e/regression/remote-session-settings.spec.ts --grep "session settings use" (1 passed)
• Pre-push workspace typecheck (32 packages passed)
• Isolated screenshot checks at fdd8abc9df: horizontal, vertical, and mobile passed (3/3); confirmed inactive tabs while settings is open, unchanged persisted tab list, and restoration via both Back to app and clicking the same session tab. Base captures reproduced the active-tab issue (3/3). The existing remote-session settings regression also passed on port 4575 (1/1).

Follow-up

A separate PR will make full-screen settings a dedicated route and remove the settings-specific tab matching guard.

[Brendonovich]

Follow-up: #45365 makes full-screen settings a dedicated route and removes the settings-specific tab matching guard. It is stacked on this PR.