How to allow a call recorder app access to call logs? How to allow a call recorder app access to call logs?
Since Android 9 (pie) Google Play has forbidden apps that are not the primary telephony app to access the call logs. The other problem seem to be that the phone recording call quality especially of the party on the other end has seemed to be severely degraded since the prior Android version.
For context, read Google Play Store Changes SMS and Call Log Policy.
Related post: Access the call-log to complement what has been banned by policy
You can't unless your device is rooted or if you are running Android 8 or earlier



Details 

Call logs

Thanks to Irfan who commented 


  On Android 9+ an app can read call logs only if it holds READ_CALL_LOG permission, which is intended to be granted only to the apps registered as default phone app (on Android 10+ it also requires whitelisting restricted permissions during app installation). Additionally apps published on Play Store cannot hold READ_CALL_LOG permission if they aren't capable of being used as default phone app which includes call recording apps. 
  
  For the same reason some call recording and other apps which need to access call logs or ongoing call's phone number publish two different versions of their apps; one on Play Store (without READ_CALL_LOG permission) and the other with the said permission. 


Call recording


Android has blocked call recording from Android 9 onwards (country specfic) 
. This has been resisted by several users as you can see in the issue tracker.
Only silver lining is that at some point of time it may be restored in future versions as mentioned in the issue tracker



  Our development team has been adding call recording APIs on their road map.  Its something that we would like to address in a future version of Android.  However due to the security and privacy implications of such APIs it is not something we can deliver for the Q release.



Without root, you cannot overcome these limitations - poor quality of recording, one sided recording, caller identity not being tagged (as in the related question which you linked). You can see these complaints in the latest reviews of the app you linked. 
Side loading an older APK isn't going to help if you are on Android 9 or above, since OS itself is blocking it. Some call recorders like Boldbeast have made Magisk modules to overcome these limitations. On OnePlus devices, you can similarly record using a Magisk module. 
If you don't want to root your phone, star the issue tracker and hope that call recording and maybe access to call logs is restored in future versions