What is the reaction between NaOH and urea?
Urea can be attacked by nucleophiles like any carbonyl. The immediate intermediate is a tetrahedral orthoacid which will break down to liberate ammonia once. The same process can be repeated a second time to liberate the second molecule of ammonia.



Technically, this is a hydrolysis catalysed by hydroxide. Hydroxide may be the reactive species but it is regenerated in the course of the reaction.

For urea to tautomerise to ammonium cyanate, a significant rearrangement and breaking a $\ce{C-N}$ bond would be required. Neither is likely in any way.