I also don’t agree with that post that states to let your new hens integrate with your original flock. You bought this hen because she was broody. Let her hatch some eggs. Put her in that crate with fresh hay and wait three weeks till they hatch. In my opinion you did absolutely nothing wrong. Just know from now on to have your broodies in a separate place, even if one of your original flock hens go broody. Always keep broodies separate.

Good luck and keep us posted.
I have a broody at the moment too, just three weeks left. Hope everything goes good with yours