I would attach it if you can. A free standing patio cover has very little chance of surviving without some tricky bracing.
Which essentially takes away the advantage of usability of a free standing structure.
Let me post a couple pics, built one last week. It looks like it is free standing, but is anchored to two different buildings.
I want to show you what I did to anchor it and may give you some ideas.
First photo, see I am dealing with stucco siding, I just cut a slot into siding to slide the beam in and attach it to house framing .... And patio cover is 16'x24' ... 14' down I did same thing on that end.
Will keep it from back and forth lateral movement.
Not exactly pretty, but has potential to put a lattice roof over it ... make it look like you meant to do it.
second photo, That is just attached to a storage shed in the back. It is not 16' wide, is only one way to utilize it, run the brace on a diagonal and it stops side to side movement on that end.
3rd, photo is a problem child. Is only a 6' 2x4 that stops the side to side movement at that end, we just tossed it in there to prove it will stop the movement.
Think we will have to build a wall there or something similar, then turn the 40 year old door around to open in other direction so you not walking into a wall.
Door wont survive so we just added a change order to cost of project.
But we need this bracing to support a patio cover. Only other option is to cross brace the post, then may as well have walls and a doorway and turn it into a garage.
Just 3 different ways I have used to brace a free standing, maybe you can use or improve on them for your situation.