If you don’t have it already, highly recommend the Merlin Bird ID app by Cornell Labs. That’s where I’m pulling pictures.

One reason a lot of people default to Coopers is because they’re pretty common in suburban areas. Not sure what kind of area you live in though. In looking at your pic vs the app’s pics of Merlins and Coopers, I’d say it’s close. The one thing that is making me question the Merlin designation is the eye color. All of the pics in the app of Merlins show a fully dark eye, and your pic suggests a yellow eye, though I grant that it’s grainy (not a criticism! Bird photography is very tough in the best of circumstances and I’m certainly no more skilled). Coopers do have yellow eyes, or at least some of them in the pics do; some are quite red, wow. Same with sharp shinned, and they are smaller. The other distinguishing factor I’ve read about between coopers and sharp shinned is the head shape; I believe it’s sharp shinned that have a very round head. So, all things considered, if she was smaller than a crow, I’d probably lean toward sharp shinned at this point.