Tiles in the Background Tasks tab should show start/finish timestamps

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

When I view the Background Tasks tab in the Claude Code desktop app for macOS, some tiles indicate errors that happened hours ago: there is no way to tell whether the error is fresh or not. So it would be helpful if each tile had a timestamp.

Proposed Solution

It would be helpful if each tile had a timestamp.

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Interactive mode (TUI)

Use Case Example

_No response_

Additional Context

_No response_