Hello Pierre, and welcome back to our community!
This is a very interesting question, and the USB RTC could also be useful for other projects, so thank you for posting all its documentation here.
From what you wrote, I think (assuming that the OS on the PI4 you have tested was the official Pi OS) that there are some compatibility issues between our Shake OS and the code provided for the USB RTC.
Our Shake OS, fully optimized for its designated work, is based on a modified version of what normally runs on any Raspberry Pi, so we provide OS updates when they are available (as the latest one, for example: Shake OS v0.20 image has been released!).
If the USB RTC software provides some logs, or the possibility to enable them, they could give you input on what is not working as expected, and you can try to proceed from there.
If anyone else here in the community wants to add something that I may have missed, feel free!