Live output tail in the /tasks (background shells) panel — inline + pop-out window

Summary

When a Bash command runs in the background, the running-shell indicator in the status bar and the /tasks panel it opens only show status/metadata. There's no way to watch the process's live output from within Claude Code — you have to fall back to tee-ing to a logfile and tail -f-ing it in a separate terminal. Please surface the output directly in the panel.

What I'd like

1. Inline live tail — in the /tasks slider panel, show a live-updating tail of the selected background shell's stdout/stderr (last N lines, auto-scrolling), the same stream Claude polls.
2. Pop-out button — a button on that panel to open the tail in its own resizable window, so a long-running server/build can be watched alongside the conversation without stealing the panel.

Why

• Background tasks (dev servers, builds, log followers) are exactly the things you want to eyeball in real time, but today the panel that already knows about them shows no output.
• The current workaround (cmd 2>&1 | tee /tmp/run.log then tail -f in another terminal) is manual and duplicates state the app already has.

Nice-to-haves

• Persist/scrollback the buffer so you can catch up on output that scrolled past.
• Per-shell "open in external terminal" option for people who want it in their own terminal app.