Realistically, the options on Linux are the uv way, the pyenv way (download and compile on demand, making sure users have compile-time dependencies installed as part of installing your tool), and letting users download and compile it themself (which is actually very easy for Python, at least on my distro). Compiling Python is not especially fast (around a full minute on my 4-core, 10-year-old machine), although I've experienced much worse in my lifetime. Maybe you can get alternate python versions directly from your distro or a PPA, but not in a way that a cross-distro tool can feasibly automate.

On Windows the only realistic option is the official installer.