Does ROS2 support python 3.11?

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Officially? No.

Iron requires Python 3.8.2 at a minimum (on Windows), and various versions of Python 3 on other platforms.

The newest would be 3.10.8 on macOS, but on Ubuntu (jammy), it standardised on 3.10.6.

This means that the Ubuntu binary packages (which is what most ROS users will be using to install ROS 2 Iron) will only be built for Python 3.10.6. Note that some of the core ROS 2 Python packages (such as rclpy) are mixed Python & C/C++, so using a different interpreter is not always just a matter of updating the path to the python binary.

See REP 2000: ROS 2 Releases and Target Platforms: Iron Irwini (May 2023 - November 2024) for all the details.

Note: you may be able to build ROS 2 Iron from source for your desired Python 3 version, but no one can guarantee you it will work, and it would not be officially supported.