[FEATURE] Identify Claude Desktop Instances in Tray Icon Tooltips

### Preflight Checklist

- [x] I have searched [existing requests](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20label%3Aenhancement) and this feature hasn't been requested yet
- [x] This is a single feature request (not multiple features)

### Problem Statement

Running multiple Claude Desktop instances, such as one per account, creates identical tray icons. Users cannot tell which icon belongs to the active window or which to use when closing a specific instance.

### Proposed Solution

Add a hover tooltip to each tray icon showing the account name, window title, or process ID. This would help users identify and close the intended instance without accidentally closing another.

### Alternative Solutions

_No response_

### Priority

Low - Nice to have

### Feature Category

Interactive mode (TUI)

### Use Case Example

_No response_

### Additional Context

_No response_

The issue names no files, tests, or entry point. Start by locating the tray-icon implementation and how multiple Claude Desktop processes or windows are represented; compare available account, window-title, and process-ID metadata. Done means each icon has a useful hover tooltip so users can identify and close the intended instance without affecting another.

Written by the indexing model from the issue text.