In my case, fredriksthlm's fix suggestion unfortunately didn't help. I deduced that the problem started occuring in r303 when Construct changed the way that the splash screen works.
What partially fixed the issue for me was building the game as Android Studio project then open it in Android Studio, go to "Edit - Find - Find in files" and find this line of code
cordovaInterface.pluginManager.postMessage("setupSplashScreen", splashScreen);
and delete it.
This means there might be a few seconds of black or white screen instead of the splash screen which is not ideal, but at least the ANR rate for my game went from 4% to 0.28%
Here's what Ashley said on the matter of trying to fix the issue by changing the implementation of the splash screen on Construct's part:
... I also don't want to have to reimplement a splash screen, which will be difficult to get exactly right, just to work around a bug in Google's code. Google should fix the root cause issue. I also have no idea how it could take several seconds to even display the built-in progress bar, that seems weird.
In short I don't think there's any action worth taking on Construct's side ...
The issue first occured after Construct updated the Cordova version it uses and therefore updated the splash screen implementation which appears to cause the high ANR rate. But I didn't find any information that would suggest that this exact issue affects anyone else using Cordova outside of Construct 3