* Refactor Client session state with ClientSessionState dataclass
Fixes#1068 by introducing ClientSessionState to encapsulate session management
attributes, simplifying Client.new() and preventing concurrent proxy client
context mixing through client factory pattern.
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Co-Authored-By: Claude <noreply@anthropic.com>
* Update proxy documentation for new client factory pattern
Documents the new session management behavior, client_factory parameter,
and concurrent operation safety introduced in v2.10.3 to fix#1068.
* Remove deprecation of client parameter and update documentation
- Undeprecated FastMCPProxy client parameter
- Made client_factory the advanced option for custom control
- Added detailed explanation of how client factories work internally
- Removed outdated note about proxy feature limitations
- Removed fabricated Advanced Usage section
* Re-do proxy documentation
* Fix deprecated client parameter to provide session isolation
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Co-Authored-By: Claude <noreply@anthropic.com>
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Co-authored-by: Claude <noreply@anthropic.com>
