Why are dendrites formed during dilute CuSO4 electrolysis black?
To quote a source as you also noted:


  Copper hydroxide Cu(OH)2 is metastable. It easily transforms into copper oxide CuO more stable, either in the solid state by a thermal dehydration or at room temperature, in aqueous basic solutions. In the solid state, the transformation is performed at a relatively low temperature, 423 K.


In the current case, a basic solution develops and copper hydroxide breaks down into CuO and water.

However, there may also be heat from applying the overpotential, and this could speculatively be the source of CuO observed.

More precisely related to the cathode, start by noting per this source (Lumen Learning), for example, to quote:


  Electrolysis of a solution of sulfuric acid or of a salt, such as NaNO3, results in the decomposition of water at both electrodes. Hydrogen will appear at the cathode and oxygen will appear at the anode.


Assuming on the cathode the formation of an intermediate species (like $\ce{H*}$ mentioned on StackExchange in an advanced discussion of the underlying mechanic on the electrolysis of water) upon self-reaction, to quote:


  In an alkaline electrolyte they propose the following mechanism, which only slightly deviates from the above. The intermediate species are the same, that's why they did not need to treat them separately. On the cathode they just summarised as $$\ce{2H2O + 2e- -&gt; 2{}^{-}OH + H2}$$ as the mechanism is bound to be the same.


Next, the action at the cathode of created OH- on Cu++ forms Cu(OH)2 which, in the basic conditions, results in CuO.