A pain point I noticed recently just visiting a hospital as a patient was not being able to find stuff! ECG pad thingies in this case. But they handled it so jovailly maybe it was a positive lol for a dreary night shift.
It's something I used to do internally at my previous employer, and I know it's very useful. In this case I would have to convince a doc to let me follow them around and that's an immense ask. It's also going to miss systemic, intangible issues that are not task related. It's a great thing to do for an already-established product.
You must have a doctor somewhere in your network 1 degree of separation away. Get a friend to ask for a favor to invite the doctor to a meal at a nice place, your treat. Be up front about your intent. At the right time, pitch to the doctor the idea of interacting on the job with doctor and/or staff. And don't promise the doctor any equity. Maybe free access to the product.
Doctors have to be very careful with this type of request. If they allow an unrelated third-party to view protected health information, even inadvertently, then they could be punished for a HIPAA violation. Most well-managed healthcare provider organizations would outright prohibit this unless there is a business associate agreement in place.