Feature: Improve background process visibility like CLI version

The CLI version of Claude Code made it easy to see running background processes at a glance. The VS Code extension has reduced visibility into background bash processes.

Current behavior:

• Background processes run but aren't prominently displayed
• Users only see them via system reminders or by manually checking BashOutput
• No easy way to list all running background processes

CLI behavior (better):

• Running background processes were clearly visible
• Easy to monitor status and output

Impact:
Users can forget about running background processes (dev servers, builds, etc.) because they're not visually prominent

Expected behavior:
Show running background processes more prominently, similar to CLI version. Could be:

• Status bar indicator
• Dedicated panel/view
• Clear list command like /bashes mentioned in tools

Environment:
VS Code extension (current version)