Hi Corneliu,
Thanks for your questions. Currently there isn't a documented tutorial/guide for the scenario you described. This is in part due to the fact that Private Link for Azure Web App is still in Preview. The preview is available in East US and West US 2 regions for all Premium V2 Windows and Linux Web Apps and Elastic Premium Functions. If you are able to use Private Link in your region, then please follow the tutorial in this documentation to learn how to Configure Azure Private Link for an Azure Cosmos account.
You can connect to an Azure Cosmos account configured with Private Link by using the automatic or manual approval method. To learn more, see the Approval workflow section of the Private Link documentation.
Hope that helps. Let us know if you have any additional questions.
Thanks,
Grace