I hesitated before replying, thinking that my reply was coming from my own assumptions. But truth be told, many other responders have also interjected a whole host of assumptions here as well.
Don't most of us see patients, in any setting, who are frail, with multiple comorbidities, often accompanied by a spouse who doesn't seem to be in much better shape? Who make us wonder, how in the heck are these people managing at home? Who raise our BP every time they attempt to transfer or ambulate? Who, although they do ambulate independently in their smaller home setting, are overwhelmed by navigating a larger environment like a giant parking lot/garage -- hospital layout -- clinic location?
I doubt I'm the only one who works on a hospital campus that can take 15 solid minutes to navigate, even walking at a good clip that qualifies as a cardio workout warmup.
OP's references to diabetic patients and surgical patients leave me picturing an older, higher-acuity patient population. Not the family visiting for their annual eye exam and picking out cool new frames.
Having said all that ...
OP, I am aware of clinic providers who see patients without support staff. They check patients in, obtain vitals, update histories, etc. Some nurses with clinic experience have responded here that their workplaces operate like this, at least for the later part of some workdays. Hopefully this gives you some reassurance.
I am aware that the chain of command in clinic settings can be a bit muddy, with nonclinical administrative management mixed in with clinical leadership. But I'm confident you can ask your question of a charge nurse/provider/etc. ... and get some clarification on expectations. I would suggest making your question as specific as possible: "Provider X has appointments through 7pm on Wednesdays. Are you looking for me to stay until those appointments are completed on Wednesdays? If so, I can plan on that for scheduling purposes." If you get clarification that the clinic providers are fine operating without nursing or support staff for the later part of their day and that is the way the clinic operates ... I would not worry that that there is any risk to you as a nurse.