OneNote downloaded from Microsoft Store opens with the old OneNote layout

I have the new OneNote version installed from Microsoft Store (new OneNote that recently replaced the old 2016 version), but it still opens with the old 2016 layout. I tried to completely uninstall all Office programs (including removal of the old registry keys and app data), and after I reinstalled OneNote from the Microsoft Store is was finally using the new layout. However, after I reinstalled the Word/PowerPoint/Excel bundle (I'm using Office 2019 Home Edition) and logged in, then OneNote started to use the old layout again.

In the OneNote license tab I noticed it is using the Office 2019 Home license and I think that this license information is causing the issue: in fact, if I try to select "continue for free" and relaunch the program, it temporarily opens with the new layout; however, if I relaunch it again, it opens as 2016 again.

In 2019 OneNote wasn't free, and it was included in the 2019 Home license, but now the new version is free and there's no need to associate the 2019 license to it. So I would like to continue using the 2019 license for Word, Excel and PowerPoint, while keeping the free version of OneNote.

Basing on my tests, it seems it is not possible, as the license information is shared by all Office products, and you cannot specify different licences for OneNote and for the Word/Excel/PowerPoint bundle (from my understanding, it's basically a registry key that is common for all Office products).

Do you have any suggestion?

Thank you