Well your mucosa is more exposed than it normally is. Your mouth is acting like a receptacle, particularly when you're not wearing a dental dam. The probability that a larger pathogen-containing droplet will randomly fall in is much higher.
Larger droplets normally fall straight to the ground. Smaller droplets can be sucked in by breathing in no matter what, so the probability for those is equivalent to just being near someone. However, depending on the pathogen, risk can scale much more than linearly with droplet size. Overall risk is probably in the ballpark of an unmasked in-your-face shouting match with someone.
Then as someone else mentioned, any fomites can transfer from anything non-sterile that the dentist or assistant touches. There can also be aerosol-generating procedures in other rooms, though the robot wouldn't help there (they'd need a negative air pressure system.)
I think OP was wondering whether any studies have been done to demonstrate a correlation between dental operations and infections. It does seem needless to worry about it until you have some idea of effect size.
Those are likely to be pathogen-specific. The paper I linked for instance has a reference that dentists have a 10x risk of chronic Hep B than the rest of the population, but that doesn't translate to Hep C.
Larger droplets normally fall straight to the ground. Smaller droplets can be sucked in by breathing in no matter what, so the probability for those is equivalent to just being near someone. However, depending on the pathogen, risk can scale much more than linearly with droplet size. Overall risk is probably in the ballpark of an unmasked in-your-face shouting match with someone.
Then as someone else mentioned, any fomites can transfer from anything non-sterile that the dentist or assistant touches. There can also be aerosol-generating procedures in other rooms, though the robot wouldn't help there (they'd need a negative air pressure system.)
This discusses some of the risks, but mostly from the standpoint of protecting the providers from the patients: https://www.ncbi.nlm.nih.gov/books/NBK589669/