It is possible to install old APK via link from Google Play Console. This way you install straight from Play Store rather than downloading the APK. This also works with app bundle which allows you to get optimized APK for your device.
- In Google Play Console go to Development tools > Internal app sharing > Manage Testers
- Add all testers you want to allow access to install old version of the app
- If you upload app bundle you can go to Release management > Artifact library > Explore on the version you want.
- The link shall be listed in Internal app sharing section. Here is the format if you cannot find the link (Be sure to replace to your applicationId and the versionCode for your app)
https://play.google.com/apps/test/applicationId/versionCode
- When you click the link on you device for the first time play store will say Internal app sharing is not enabled.
- To enable Internal app sharing open Play Store > Settings
- Scroll all the way down and keep clicking on Play Store version to enable developer mode
- Once developer mode is enabled you will see Internal app sharing switch in the settings once enabled you will be able install your app from the link.
FYI: I have seen some version not working if they were not released to production track. I am able to install all my production tracks also any active artifacts listed in Artifact library in Google Play Console. This should be enough if you are trying to test upgrade scenarios.