I want to download all old versions of an app on Google Play Store since 2017. I looked at APKCombo and APKPure, but neither of them has so old versions. It does not exist on APKMirror.
Now it is possible. They added "Manage Releases" tab to Google Play Developer Console. From Artifact Library under the Release Management tab, you can download your app's APK.
You need to have the necessary permissions to see the download button next to your artifacts. If in doubt, try the root account.
THE ANSWER IS OUTDATED. NOW THIS IS POSSIBLE, CHECK @tesla's AND @olleh's ANSWERS.
FOR THE NEW 2020 GOOGLE PLAY CONSOLE, SEE ANSWER FROM @IonicBurger
No, unfortunately.
The Android Developer Console is a real disaster, everywhere you look there is something that needs to be fixed or improved, being this issue you mention one of them. Unfortunately for the time being you're out of luck. Unless Google enables this, you cannot download old APKS's. I suppose you could recompile the old code, but I guess you don't have that either and that's why you are here :-)