Update terminal tab title to show current/last working directory

When running Claude Code in a terminal, it would help to have the tab title reflect the current working directory (or at least the last path segment). This makes it much easier to identify which tab/session is which when running multiple Claude Code sessions across different projects in separate terminal tabs.

Suggestion:

• Set the terminal tab title to the current working directory (or basename of it) when Claude Code starts, and optionally update it if the directory changes during the session.
• Bonus: could include a short status indicator (e.g., idle/running) alongside the path, similar to how some other CLIs update their tab title dynamically.

Motivation: With several terminal tabs open for different repos/sessions, it's hard to tell them apart at a glance since tabs default to generic shell titles.