@gardencat - They are close in looks. If you noticed I changed the title as I Googled Purple and House Finches. Purple Finches have a lot more red over their bodies while the House Finch is mostly the head and some on the upper breast. The Purple's beak is a little longer and the House's head is rounder. So I think that this is a House Finch based on its beak and head shape.
I love this -- the finch (purple? house? I could never tell them apart but your explanation helps!) face in focus, the softness of the moving parts, balanced in air with the colors complementing the bird as the background.
https://www.audubon.org/news/house-finch-or-purple-finch-heres-how-tell-them-apart
https://www.audubon.org/news/house-finch-or-purple-finch-heres-how-tell-them-apart