Access Web Apps have been deprecated and are being turned off on October 1, 2018. Here is the announcment from last year. As has been pointed out on this thread, the backing store for AWAs is SQL Azure and you can obtain the SQL connection strings through the Access client.
I have created a PowerShell script to make it easier to migrate AWA data (retains relationships, imports images, handles primary names, etc) to CDS available at http://aka.ms/cdsimport.
You can also obtain the .dacpac file for an AWA by saving out the database as a Snapshot file from within Access. Instructions are available here.
At this time, there are no plans for PowerApps to connect to Access Desktop databases (.accdb files). You can use the on-premises gateway to import data from these files to CDS. There are many tools available for moving Access Desktop database data to SharePoint or SQL, a common location where both Access Desktop and PowerApps can connect to the data.