[Bug] Blue unread markers missing in standalone Claude Code Desktop app

Description

The standalone Claude Code Desktop app previously showed blue unread markers/indicators for conversations or completions. These markers are no longer visible.

Context

• The [VSCode] integration added tab icon badges in v2.0.73: blue for pending permissions, orange for unread completions
• The standalone Desktop app appeared to have its own unread marker system (blue indicators) that is now missing
• Issue #30766 requests notification dots for background task completion in the Claude App, which was tagged invalid - suggesting this may be an intentional removal or a regression

Expected Behavior

Blue unread markers should appear in the standalone Desktop app to indicate unread completions or conversations requiring attention. These were previously present and are described as "invaluable" for managing multiple sessions.

Actual Behavior

No blue unread markers are visible in the standalone Claude Code Desktop app.

Environment

• Platform: macOS (Darwin 24.4.0)
• Claude Code: latest version as of 2026-03-09
• App: Standalone Claude Code Desktop (NOT VSCode extension)

Impact

Without unread indicators, users managing multiple concurrent sessions have no visual signal for which sessions need attention, making the multi-session workflow significantly harder.