We already know from TOS that Mutlitronic computers are able to develop sapience, with the M-5 computer being specifically designed to “think and reason” like a person, and built around Dr Daystrom’s neural engrams.
However, we also know from Voyager that the holomatrix of their Mk 1 EMH also incorporates Multitronic technology, and from DS9 that it’s also used in mind-reading devices.
Assuming that the EMH is designed to more or less be a standard hologram with some medical knowledge added in, it shouldn’t have come as a surprise that holograms were either sapient themselves, or were capable of developing sapience. It would only be a logical possibility if technology that allowed human-like thought and reasoning into a hologram.
If anything, it is more of a surprise that sapient holograms like the Doctor or Moriarty hadn’t happened earlier.
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No, sapience would be the right word in this case. Sentience is more for general self-awareness, whereas Sapience is more for human-like intelligence, which the Doctor (and Moriarty) express.