How come in biuret test the copper sulfate doesn't react with the sodium hydroxide?

As I understand the color change in the biuret test is due to the formation of a complex between the peptide (with more than 2 peptide bonds) and the $\ce{Cu^2+}$ ion, from $\ce{CuSO4}$. But before adding the $\ce{CuSO4}$ we add a base to our solution in this case $\ce{NaOH}$, my book says that's because we want an alkaline environment in order for the reaction to happen.


Shouldn't $\ce{CuSO4}$ react with the $\ce{NaOH}$ and then their product $\ce{Cu(OH)2}$ will precipitate?


Or at least both should happen. Every YouTube video I've seen, of the Biuret test, shows both tubes being clear and only a color change, and no percipitation.


In another case for example a Fehling's test for reducing sugars we add an extra compound (sodium potassium tartrate) in order to prevent $\ce{Cu^2+}$ reacting with the $\ce{OH-}$, why not in the biuret test?


