Flagging likely spelling and basic grammar errors are pretty much incorporated into most word processors at this point. I may or may not choose to ignore them. But they work pretty well and I'm unlikely to use an external tool.
I did write for a while for a tech site that had some Wordpress add-on that was oriented to making my writing, I guess, more friendly to an 8th grade level. I ignored it.
I mostly just rely on browser to check my spelling. In work well copy paste it to World if I really want to get fancy... I did years ago use Grammarly for my thesis and spam finally ended after years some time ago...
You're right that it's mostly just the browser. Other than one or two text editors, I don't think I even have a word processor installed on a system at this point.