Ultimately, Dooku’s status as an apprentice or not is irrelevant because Palpatine never gave a damn about the Rule of Two. Palps is the logical end result of that system - a greedy sociopath who cares only about himself and his own power with no regard to ideology or what happens when he’s gone. Palpatine had Dooku and Maul as apprentices simultaneously while mostly keeping their existences secret from each other because neither of them were intended to replace him, but to be specialized tools with different purposes. Maul was an assassin meant to kill his enemies without being traced back to him, and Dooku was there to stage false-flag attacks so he could increase his political power. Enforcing the Rule of Two on them and making them fight to be his only apprentice would have been detrimental to his personal plans, the Sith as an organization be damned. He was also totally fine with Dooku blatantly violating the Rule of Two by openly training Ventress right up until he thought Dooku and Ventress might be able to overthrow him, at which point he suddenly started enforcing it by making Dooku kill Ventress.