So I guess Avast is trying it's hand at being ransomware.

I don’t mind the various little popups that appear in the bottom right. Not even when using my paid Avast Premier. But one of the popups is a problem. The one talking about my computer being slow (when it isn’t) and how I need X product to make it faster. It’s a problem because, as it draws itself to the screen in stops and stutters, it slows down the application beneath it.

Now I thought… ok that’s just a bug in the code for those popups. It’s doing something wrong in how it draws itself to the screen and messing with the compositor (yeah, I’m an IT professional). But no… this problem only effects that one popup… the one that just happens to be trying to sell me something on the basis that my computer is slow (when it isn’t… except when that one popup is being drawn to the screen).

So what was the plan here Avast? Intentionally lag computers to make them seem slow so you could trick computer illiterates into giving you money for products they don’t need? Or else you’ll keep lagging their computers? Yeah… that’s called ransomware. And it’s one of the problems your product is supposed to solve… not create.

Displaying popups is one thing. Interfering with proper operation of a computer is another.

I don't mind the various little popups that appear in the bottom right. Not even when using my _paid_ Avast Premier
As has been told/explained a huge times on this webboard, you can disable them in the paid versions.
The one talking about my computer being slow (when it isn't) and how I need X product to make it faster
That is likely a promotional ad for CleanUp. Will that tool really make your system faster ? Yes because it removes certain rubbish. Will you notice the difference between before and after ? Unless your system has a huge amount of rubbish on it, the answer is no. Does it do anything you can't do yourself ? No, not at all. You can cleanup things manually a lot better (if you have a bit of knowledge) CCleaner is free and does a good job if you want to use a tool.
So what was the plan here Avast?
Well that is easy to answer. avast is trying to sell crap and make money over the heads of people who don't know anything/not have even basic knowledge about computers/the OS etc.