Just noticed that the "LastVersion" file in the profile folder, as the name suggests, gets updated when the profile is opened with (another version of) BAS e.g. from 114.0.5735.91 to 117.0.5938.63. Therefore it's not suitable for our need to determine the original version of which a profile was created.
But at least can be said what was the latest BAS version that worked with it ;)
I there any option to use APK (Android APP) in BAS?
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It is possible, but not all and through the Emulator
https://developer.android.com/studio/command-line/adb