@Andrey Enev Welcome to Microsoft Q&A Forum, Thank you for posting your query here!
Could you please try to check from the kudu console by updating your web app name in the below URL:
https://{YOURWEBAPPNAME}.scm.azurewebsites.net/DebugConsole
Then click on the site folder. Then you can either download the wwwroot folder or download the bot source code directly as shown below:
Hope this helps. If you have any follow-up questions, please let me know. I would be happy to help.