It will seriously vary by where you end up. In my residency (in academia) a lot of surgeries were performed by the researchers (and a lot of MD surgeons) with vet/vet tech anesthesia support, BUT we also did a lot of the surgeries for them (endometrectomies, c-sections, vascular access port placements, central line cutdowns, etc) or got to scrub in with them (cystectomies/biobladder replacements, etc). At the pharmaceutical company where I spent the last portion of my residency they had veterinary surgeons doing all of their experimental surgeries - primarily placing access ports (GI, vascular, etc) but also figuring out new experimental surgical models for things. They also did a lot of spay/neuters for adoptions of retired research animals. At a medical device company I interviewed at the veterinarians did all the surgeries - implanting heart valves and new medical devices, essentially developing the models for the new devices and how to implant them, and then going on to teach human MD surgeons how to do it. At my current position (academia) it's primarily the researchers performing surgeries 🙂cryi🙂. I'm lucky to scrub in with the residents on our adoption spay/neuters or emergency dehiscence repairs or similar.
I think if you're looking to do surgery and are flexible you can definitely find lab animal positions that do a lot of surgery, but it's definitely not universal.