[Bug]: RouterLLM bypasses model selection for async completions

Bug Description

RouterLLM overrides only synchronous completion() in openhands-sdk/openhands/sdk/llm/router/base.py:57-95. Normal async agent execution calls inherited LLM.acompletion(), so routing selection is never performed and the router's placeholder model is used instead of a configured child.

The synchronous path also writes the selected child into shared Pydantic field active_llm before dispatch. Concurrent calls can overwrite one another between selection and use. Meanwhile __getattr__() at :113-117 ignores active_llm and always delegates to the first configured model.

Expected Behavior

Sync and async calls should perform identical per-request routing, without dispatch depending on mutable shared selection state.

Actual Behavior

An independent, self-contained reproducer is posted in the issue comments. Save
it as /tmp/repro_4660.py, then run:

uv run python /tmp/repro_4660.py

On SDK commit 6d3881035, it exercises the real inherited async completion path and real TestLLM children; an intentionally unreachable local endpoint makes wrong dispatch deterministic and prints:

async_error_type=LLMBadRequestError
attempted_model=openai/router-placeholder
select_llm_calls=0
selected_child_remaining=1

Suggested Implementation

Resolve the selected child into a call-local variable through one shared helper, then delegate immediately from both completion() and acompletion(). Keep active_llm only as a compatibility field/accessor for now; removing it is public API work and requires the SDK deprecation runway.

Acceptance Criteria

• Async completions select and invoke the expected child LLM.
• Sync and async paths share selection/validation behavior.
• Concurrent calls selecting different children cannot cross-dispatch.
• Token callbacks, call context, tools, retries, and kwargs reach the selected child unchanged.
• Invalid selector keys fail deterministically.
• Existing public constructor/serialization compatibility is preserved.

Version

Current main at 6d3881035. Existing searches found no open issue covering async router bypass.

Start in openhands-sdk/openhands/sdk/llm/router/base.py, especially completion(), the inherited acompletion() path, and getattr; run /tmp/repro_4660.py with uv run python /tmp/repro_4660.py. Done means sync and async calls share selection behavior, concurrent requests dispatch to their own selected children, and callbacks, context, tools, retries, kwargs, invalid selectors, and public compatibility remain correct.