Nah they just used the poors to take care of it.

Which I guess is still sorta true today.

The "that isn't native" part is mostly a US problem. The reason they aren't native here is that Europeans brought over the same turfgrass species they'd been using at home.

"Kentucky bluegrass," for instance, is actually native to Europe, despite the name. Ditto for fescue, bermudagrass, etc.

And they were spraying all kinds of nasty shit...

Yes they used literal shit, both animal and human.

...on grass that isn’t native...

I can't answer that but it really wouldn't surprise me. The ruling class commonly imported plants and animals from all over the world.

...to make it look pretty?

No pictures exist, obviously, but I'm quite sure that groundskeepers were doing whatever was necessary to make their Lords estate look as good as possible.