Disabled splash screen, have Unity Plus, WebGL still freezing when running in background

I require my WebGL application to be running when switched to a different tab in a browser and there is a setting to solve that in Unity: run in background. However, "run in background" only works after the Unity logo has been presented to a user. In other words, if I open the application and instantly switch to another tab, wait no matter for how long and switch back, I will see the splash screen first and only then I can switch tabs and hope that the application will run in background. That is probably done on purpose so that a user does not miss the splash screen.

My problem is that even after removing the Splash screen (since I have got Unity Plus), the application is still not running completely in background. It stops for the same number of seconds, even though this time it is not presenting the splash screen. It did disable the splash screen, but running in background only triggers after the invisible splash screen animation has been played.