fix(llm): preserve event loop in sync cache

[FU-max-boop]

Description

Preserve caller-owned asyncio state in the synchronous LLM cache middleware. The middleware previously installed its private event loop as the thread default, then either left a closed loop installed after a cache miss or leaked the loop on an early cache-hit return.

Related Issues

Closes #2478.

Proposed Changes

• Keep the middleware's private event loop isolated from the caller's default loop.
• Close the private loop in a finally block on cache hits, cache misses, and exceptions.
• Add regression coverage for all three lifecycle paths.
• Add the required patch-level semversioner change record.

Checklist

• I have tested these changes locally.
• I have reviewed the code changes.
• I have updated the documentation (not necessary for this internal lifecycle fix).
• I have added appropriate unit tests.

Validation

• uv run poe check
• uv run poe test_unit (317 passed)
• Baseline mutation check confirms the new regression assertion fails against current main.

Additional Notes

The asynchronous cache middleware is unchanged because it already runs in the caller's active event loop and does not create or install a private loop.