fix(agent-manager): show live subagent tab activity

[marius-kilocode]

What Problem This Solves

Subagent tabs in Agent Manager kept a fixed task icon while the session was running, retrying, or waiting for input. This also affected async subagents opened from the background-agent strip, so their tabs did not provide the same progress and outcome signals as normal session tabs.

Why This Change Was Made

Use the existing activity resolver, icons, colors, and translated labels. Read activity from the parent session provider so events received before the inspector opens are not lost. Keep the inspector's separate chat provider so selecting a subagent does not replace the parent conversation.

User Impact

• Show animated spinners for running and retrying subagents.
• Show the normal needs-input, completed, and error indicators, with matching tooltips.
• Update inactive tabs and preserve the idle task icon.
• Keep tab selection, closing, and reopening independent of the parent chat.

Evidence

• Extension build, type checks, lint, Knip, formatting, and the Kilo marker guard passed.
• All 36 focused tests passed, including the real subagent panel mounted after activity events and reopened after completion.
• All 4,494 extension unit tests passed on rerun without code changes. The first full run hit the existing PR-comment render test's 5-second timeout; that test also passed in isolation.
• Isolated VS Code checks passed for all six states, inactive-tab updates, blocking versus nonblocking questions, disconnect/reconnect, async-agent opening, spinner animation, and closing/switching tabs.
• UI checks used deterministic session events, not live model requests. The screenshots contain only test labels.

Running, retrying, and waiting for input:

Completed, error, and idle states after reopening the tabs: