Enhance AsyncClient for Flexible Session Management in Text Generation Client

[BenHaimItay]

Updates the AsyncClient to efficiently manage sessions for both direct await usage and within async with blocks, improving flexibility for various async operation scenarios.

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[Narsil]

LGTM.

Thanks for the fix. FWIW we're soft deprecating this client in favor of https://huggingface.co/docs/huggingface_hub/package_reference/inference_client (Which should have more or less the same features and more important has more broad support in the HF ecosystem).

[Narsil]

Seems the tests are not passing though.