Hello @Stefano Giostra , Thank you for reaching out and apologies for the delayed response here. Your folder structure is correct and you are importing the modules using absolute references and you have __init__.py in your shared code folder which is also correct as per the documentation. I tried publishing my app with a similar set-up but I did not face any issues. We might need to look need to look at the logs to debug the issue further.
To answer your questions
How can I verify if mysubdir was uploaded?
When doing a func azure functionapp publish you can add a --list-included-files flag to check which files were uploaded.
Second question I'haven't understood how I can see the function logs?
You can go to your Function on the portal, under developer section in Code+Test you can stream any instance logs. You can also go through this documentation to enable Application insights and Live Stream logs.

Hope this helps! Please let me know if you have any additional questions. Thank you!