feat(BA-2325): Apply client pool to synchronous API session

[rapsealk]

Follow-up of {#5223, #5253} and resolves #5820 (BA-2325)

Checklist: (if applicable)

• Milestone metadata specifying the target backport version
• Mention to the original issue

[HyeockJinKim]

I'm not sure if the name "own_session" is appropriate.

[rapsealk]

Renamed it as _has_aiohttp_session_ownership.

[Copilot]

Pull Request Overview

This PR implements client pool functionality for synchronous API sessions, following up on previous work in issues #5223 and #5253. The changes introduce a new synchronous client pool implementation and refactor the existing session management to support both async and sync client pooling.

• Modernizes type annotations from legacy typing module to built-in types
• Creates shared sync worker thread utilities for managing async operations in sync contexts
• Implements SyncClientPool for connection pooling in synchronous API sessions

Reviewed Changes

Copilot reviewed 6 out of 6 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Description
src/ai/backend/common/types.py	Updates type annotations to use built-in types and adds Sentinel enum documentation
src/ai/backend/common/sync.py	New module providing SyncWorkerThread for async-to-sync operation bridging
src/ai/backend/common/clients/http_client/client_pool.py	Refactors client pool architecture with base class and adds SyncClientPool implementation
src/ai/backend/client/types.py	Removes duplicate Sentinel implementation, now using common version
src/ai/backend/client/session.py	Refactors session classes to use shared sync utilities and support injected aiohttp sessions
changes/5841.feature.md	Adds changelog entry for the feature

Comments suppressed due to low confidence (1)

src/ai/backend/common/sync.py:1

• The execute method is designed for coroutines that complete and return a value, but _cleanup_loop is an infinite loop coroutine. This will block the worker thread indefinitely and prevent it from processing other work items. Consider using a separate task or thread for the cleanup loop, or restructure the design to avoid blocking the worker thread.

import asyncio

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