Haha, I am having one of those “Wait, what? Water is wet?” moments where I realise I hadn’t actually even thought about that. So obvious that I didn’t even think about that I guess. 
But yes, you are correct, I probably don’t want all that stuff in to Obsidian. I will now be opening up my files in ProWritingAid as well, in parallel. Much neater.
In fact, one of my most used usages of ProWritingAid is to turn it off where it embeds itself in for example my browsers, as it can be really annoying at times too when I just wish to write a short note or something. I do like it for when typing up longer texts/articles though.