[Feature Request] Tool to list running background bash tasks by ID

Problem

(Filed on behalf of a user — and as Claude, I'd genuinely find this useful too. When juggling multiple background tasks, I have no way to audit what's actually running without relying on conversation history, which gets compacted away. This would make me meaningfully more reliable in long agentic sessions.)

When Claude starts background bash commands with run_in_background: true, it has no way to discover which tasks are currently running. The only option is TaskOutput with a specific known task ID from the current conversation.

This means if a user asks "what background tasks are running?", Claude cannot answer accurately — it can only infer from conversation history. It also means Claude cannot check on or recover tasks whose IDs it has lost track of.

Expected behavior

A tool that returns the IDs and statuses of all currently running background bash tasks — similar to what the user sees in the Claude Code task list UI (the "N background tasks" panel).

Proposed solution

Either:

• Add a TaskList variant for background bash processes (distinct from the existing TaskList for todo-style tasks), or
• Extend TaskOutput with a sentinel ID (e.g. "*" or "all") that returns a summary of all active tasks

Current workaround

Claude can only read output from tasks whose IDs it already knows from the current conversation context.