[FEATURE]: Show MCP tool activity in the TUI sidebar #43717

Feature hasn't been suggested before.

• I have verified this feature I'm about to request hasn't been suggested before.

Describe the enhancement you want to request

The sidebar shows MCP server connection status, but not current MCP tool execution. While a call is running, it is difficult to tell whether it is active, stalled, or complete, and elapsed time is not visible.

I have a local patch exploring a narrow MCP Activity panel in the existing sidebar. It shows active MCP calls, progress when reported by the server, elapsed duration, completion status, and a bounded recent history. The same lifecycle covers direct MCP calls and MCP calls made through code mode. It is not intended as a general tool activity panel. This also aligns with the MCP specification itself, which defines progress notifications as a first-class pattern for long-running operations (https://modelcontextprotocol.io/specification/2026-07-28/basic/patterns/progress) — servers can already report progress, but today there is no place in the UI to surface it.

There is related prior art: #9655 and PR #9658 proposed broader sidebar activity; #26328 covered MCP progress; #22144 covered tool timestamps and live duration. This proposal narrows those ideas to MCP execution in the current sidebar architecture.

Before preparing a PR, I would like design direction from maintainers:

1. Does an MCP-specific activity panel belong in the sidebar?
2. Should completed calls remain briefly, or should the panel show active calls only?
3. Are MCP lifecycle events the right boundary, including code mode calls?