Hi KK,
Please consider to use a private link between the App Service and the Azure SQL Database instead of exposing the database to the Internet. You may need a premium App Service plan to use VNET integration as Standard plan does not allow it.
Your desktop users would be able to connect to the Azure SQL Database using a VPN or using Express Route.
Here you will find how to migrate your web application to Azure App Service.
If your database has a size of a few hundreds of GBs you can consider migrating it to Azure SQL using Data Migration Assistant. For bigger databases, my suggestion is to use Data Migration Service.