The above recommended solution of turning on 'Improve data source experience and Microsoft Dataverse views' didn't work for myself. However, I did come across the issue and thought it strange. I tend to use a macOS device, but noticed my colleague who works on a Windows device and is in the same Microsoft365 environment didn't have the issue. After creating the PowerApp on my macOS device, the Data Sources button was still not present within my current PowerApps even when logging into MS Edge on a Windows device.
To troubleshoot the issue, I created a blank PowerApp from scratch using MS Edge on a Windows device - straight away I noticed the Data Source button was there! Subsequently, when opening the same PowerApp on my macOS device, the Data sources button was still present.
So it looks like in my instance it's all to do with what OS and Browser was used to initially create the PowerApp. If I used a browser within macOS to create the PowerApp, then the Data Source button was not present (and never will be). If I create the PowerApp on Windows then the Data source button is present and persists.