Does the fast become invalid, and is a make-up day obligatory for someone who involuntarily ingested water while having their teeth cleaned at the dentist during the daytime in Ramadan?

Your fast is valid as long as you did not intentionally swallow the water, for Allah Almighty says: "And there is no blame upon you for that in which you have erred, but [only for] what your hearts have intended." It is advisable to postpone treatment that may involve something reaching the stomach until after Maghrib, if possible.