Hi Piotr,
Happy New Year!
After doing more research, I found out that OneNote client access to notebooks on SharePoint Online and OneDrive for Business is not a feasible feature for Office 365 Business Essentials users. However, you can still use your email address as Microsoft account to access notebooks on OneDrive. We’re sorry for the inconvenient.
Here is the service description for your reference:
Office Applications Service Description
Thanks,
August