At https://phys.org/news/2023-01-billions-celestial-revealed-gargantuan-survey.html … the answer to the title is too many to count. However, a survey of the galactic plane of the Milky Way has identified a dataset of 3.32 billion celestial objects – in just one part of the sky as seen from the southern hemisphere. In fact, the Milky Way contains hundreds of billions of stars. Yes, billions. And the Milky Way is but one galaxy. The numbers involved are mind boggling.
The survey used the Dark Energy Canera instrument from an observatory in Chile, in order to capture the southern galactic plane in detail. For more info see https://doi.org/10.3847/1538-4365/aca594 .. [Astrophysical Journal Support Series, 2023].