client.clone() does not properly clone session

[MarshalX]

The clone method clones HTTP headers including the current access token, but does nothing with the refresh token. So the bug will rise when exp of clones instance passes. The client will not be able to refresh the session automatically.

The correct fix is not only about coping session-related fields. We need something shared between all clones. Because client A (original) could refresh the token on some request. This will invalidate refresh token. The client B (clone of A) will not be able to refresh the token because the refresh token was used already. And the new one only belongs to client A... Tokens should be shared between all clones.

This affects all methods that use .clone():

• with_labelers
• with_bsky_labeler
• with_proxy
• with_bsky_chat_proxy

P.S. Nobody reported that issue