Remove temporary async SDK adapter when aioboto3 supports modern Botocore

[dkropachev]

Context

PR #114 upgraded Boto3 and Botocore to a release family with native DynamoDB vector models. The latest released aioboto3 (15.5.0) pins aiobotocore==2.25.1, which caps Boto3 and Botocore below 1.40.62, so it cannot coexist with the required botocore>=1.43.64 floor.

Until aioboto3 catches up, Alternator client uses a small private, client-only session adapter backed directly by aiobotocore. The adapter is an implementation detail and does not add a public API.

Upstream tracking: terricain/aioboto3#404

Removal criteria

Remove the temporary adapter after an aioboto3 release:

• supports the Botocore minimum required by this project (currently >=1.43.64)
• supports every Python version supported by this project
• resolves together with all project extras and development type stubs

Work

• restore aioboto3 to the async extra
• switch async client construction back to aioboto3.Session().client(...)
• remove the private adapter and its adapter-specific contract tests
• retain the existing public async client API and lifecycle behavior
• update documentation and run unit tests across Python 3.10–3.14 plus the integration suite

[dkropachev]

The temporary private adapter is implemented in #116. Keep this issue open until a compatible aioboto3 release lets us remove it and restore aioboto3 behind the unchanged internal session boundary.