Can ROS2 run on macOS big sur 11.5.2?

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The last version to be mentioned explicitly in REP 2000: ROS 2 Releases and Target Platforms was Mojave, and I haven't heard of any work regarding porting to any newer versions.

That doesn't immediately mean it can't be built on newer versions of the OS of course.

See macOS support in ROS 2 Galactic and beyond on ROS Discourse for a recent(-ish) discussion about this, and the linked ros2/ros2/issues/1148.

The last update to that issue states:

Various issue, specifically related to Big Sur and/or Apple silicon (M1 cpu) break the build.

but that is the status as of 2021-06-02. Things may have changed in the meantime.

Edit: I forgot about the work of the RoboStack devs. See RoboStack/ros-galactic and RoboStack: Using ROS alongside the Conda and Jupyter Ecosystems on any Linux, macOS, Windows & ARM. You're going to need Conda, but IIRC, you should be able to install (at least some parts of) ROS 2 Galactic on macOS that way.

Note: this is not equivalent to "official" support for macOS. But it's as good as it's going to get for now I believe.