When in doubt, add the #!/bin/env python3.10 shebang to the top of your script to ensure the version it's running on is the same as the version you're writing the script for.
If I build an application on Linux I need to specify a glibc version or a PHP version or a Java version in some way as well. I don't see what this has to do with Python. Good luck running a jar built with JDK19 on JRE8, or an executable linked against glibc2.36 on Ubuntu 18, or a Python file written for Python 3.10 on a system that comes with Python 3.6.
Statically compiled languages come with their own problems (note that C++, Go and Rust also have system requirements, I've had to deal with a Go executable that would not work in a musl environment and a Rust executable that I needed to build on Ubuntu because the compiled version from my Manjaro laptop linked a against a libc version that was too recent).
If you need dependencies, specify and install them. If your only dependency is the interpreter, document it, specify it in the shebang, or deal with it. Python 3 is completely backwards compatible in my experience, it's only the programs that stuck with Python 2 for a decade that have trouble running on modern machines in my experience.