On a phone licensing the Play Store sure. But on a Huawei phone free of those restrictions they can make it use any store they want without any special restrictions. Of course, it becomes a question what that means for security, but still.

I did not root my phone yet, and I install apps with f-droid just fine. The only thing I had to do, if I recall correctly, was enabling third party apps instalation

Try it again and watch the process closely. You'll get an additional prompt when you use F-Droid that doesn't appear with the Play store.

Indeed there is an extra confirmation step, and it freezes some processes (specifically, those that alter the screen, like red shifters)

That seems like a violation of anit-trustlaws. I'm surprised the FSF hasn't pursued this route against google.