Designer only saves the .ui file. You need to run pyside6-uic to convert that to the .py file.
It seems you didn't read entirely the OP, it does, from the Form menu, the only annoying issue is that it's not automatic when saving the ui for obvious reasons.
So probably I could make a designer plugin that does it, regardless to the IDE editor used.
There are some limitation in Designer plugins that makes this less useful than the current option.