The “old SAT” required serious vocab-focused study time. The New SAT and the ACT do not. Having a good vocabulary is still helpful for both tests – it’ll help you to grasp the full meaning of the passages, and on the few “what does this word mean in context?” problems.
But if you learn the strategy for the context problems, and if you regularly complete SAT or ACT reading passages (in official or well-regarded third party books) and make flashcards out of the words you encounter within, you don’t need to do any “vocab only” work.
It’s always a good idea to improve your vocabulary – so if you want to work through some “word of the day” apps etc., you should! But know that it’s not a cornerstone of your SAT or ACT reading score anymore. If you’re looking for more specific reading strategies, I recommend my SAT reading strategy crash course.