Boise Anesthesia, PA covers St. Alphonsus and Boise Anesthesia Associates covers St. Luke's. Each have a flagship hospital in town as well as a few smaller facilities. St. Al's is level 2 trauma, St. Lukes is level 1 peds trauma. Both groups are very supervision-heavy. I think hearts are solo but am not positive about that. When I was poking around a few years ago, BAA was only hiring associates, not partnership track. My impression was the partners were well-compensated but worked hard. No idea how things have changed since then (I was looking pre-COVID).
There's also a small VA w/ supervision. Not sure about smaller groups that may cover smaller surgery centers.