While there are no official wheels for 3.13, it is possible to compile mediapipe for python 3.13. I have done so for my Jetson Nano (took a while to compile).
It requires modifying a couple files (namely, updating some Bazel workspace files to look for python 3.13, and adding a requirements_lock_3_13.txt file, and changing the package versions to match what is available in python 3.13).
I tested it, and it works fine. At least with the hand gesture example. From what I've used it for, it doesn't seem like there are any overt/major incompatibilities with Python 3.13.
You'll need Bazel to build it, and GCC 11+, and Protobuf Compiler/protoc >= v25.