I haven't checked for PyQt/PySide but the Linux wheels are more-or-less distro-specific, they're not manylinux wheels. I don't think a compliant manylinux wheel (i.e. one that includes all libraries beyond those of the manylinux2014 reference platform) is even desirable, because gtk doesn't really like being shipped with applications, it wants to load plugins and themes from the system etc. Qt is similar - a Qt app that ships its own version of Qt will always have issues fitting in with the system Qt LAF.
It of course depends on what the target is, exactly. If you don't care about looking "native", for whatever little meaning that has had for the past decade, you can just use whatever theme you fancy with Ttk. The theming engine might not be as powerful as Qt's, but it's certainly good enough for emulating a modern flat-look UI: https://github.com/israel-dryer/ttkbootstrap
Although, I'm guessing now that Python and Rust are becoming BFF, https://tauri.app/ will become a more and more attractive option.