async tools work outside AsyncToolset via activity-scoped manager

[longcw]

Summary

Extract _AsyncToolManager from AsyncToolset so async-tool lifecycle (AsyncRunContext creation, background task spawn, duplicate handling, progress-reply coalescing) is usable independently of the toolset wrapper. Each AgentActivity now owns one manager (on_duplicate_call="reject"), and at tool dispatch any tool whose signature includes AsyncRunContext is routed through it. No upfront grouping or AsyncToolset wrapping needed — a bare @function_tool async def foo(ctx: AsyncRunContext, ...) in agent.tools Just Works.

Backward compatibility

• AsyncToolset(tools=[...]) unchanged — _wrap_tool body now delegates to its own _AsyncToolManager but external behavior (duplicate handling, progress narration, cancel) is preserved.

Example

from livekit.agents import Agent, AsyncRunContext
from livekit.agents.llm import function_tool

class MyAgent(Agent):
    @function_tool
    async def search_news(self, ctx: AsyncRunContext, topic: str) -> str:
        await ctx.update(f"searching the news for {topic}...")
        await asyncio.sleep(10)
        return f"Top story on {topic}: nothing dramatic happened today."

No AsyncToolset wrapping. The agent acknowledges immediately via the update, then narrates the final result.

See examples/voice_agents/basic_agent.py for the full example.