OP your post made it seem like you're asking who's researching/inventing actual surgical technique, as in - inventing new ways to do surgery.
The answer is very few people do that, and the ones who do are practicing surgeons who are experts in their fields an have 10-20+ years of doing surgery under their belts and yes - they generally do new surgical techniques on humans. They may conceive of an idea, practice it in a lab on an animal and/or cadaver, and then proceed to do it on a human, but they are extremely high volume or extremely narrowly tailored surgeons that do lots of surgery. They are not sitting and inventing this stuff in a lab.
If you're instead asking about equipment like who invented the Da Vinci robot or who invented the Lynx for reflux, and stuff like that - surgeons generally working hand in hand with engineers. Not medical doctors in a lab.
Surgeons who work in a lab tend to more often than not be involved in cancer research (majority) or maybe transplant or a surgical subspecialty working on a rare disease (think neurosurgeons trying to cure a very specific rare illness). Outside of cancer I do not think it is the normal for most surgeons to have more than 20% of their practice be in research. At least for the general surgery sub-disciplines (vascular, MIS, bari/foregut, endocrine, colorectal, trauma) the proportion who run a lab is probably at best 1%. Maybe its different for ENT/ortho/urology, but I really doubt it, suspect they are also around 1%, as most surgeons simply do research while having a clinical practice if that is their passion. NSG is probably the same but I could envision it being slightly higher, but I genuinely don't know. In cancer, those who have a lab are usually working on immunotherapy/chemotherapy/molecular targeted therapies and not actually inventing new ways to do surgery. They're working on augmenting therapy before and after surgery, potentially using surgery as a deliver vehicle for therapy, etc.
There is a 2-3 year surgical oncology research program at the NIH which is composed mostly of surgeons who now strictly do bench research. Honestly, I would classify them more as medical oncologists/immunologists than actual surgeons at this point, but that route does exist. It is an incredibly slim minority and a rare breed of human that takes that road. But they're crazy geniuses.