Based on what we can see there is no reason to think it is different outside the observable universe. Everything is the same in every direction we look, galaxies and more galaxies. While you can never prove it, looking at our patch suggest the rest might be like this too. We have no reason to think if we went further out we would expect the galaxies to taper off. And the measurement of the observable universe’s curvature is flat insofar as our best measurements can tell, that is consistent with infinite, although not a guarantee. But if it is and the rest is filled with galaxies like our patch, then yes there would be infinite stars.
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