Going to ask you a question I don't want you to answer. Is the goal of your training to lift smaller weights many times, or to lift bigger weights and get bigger muscles?
I assume it's the latter of those two. Volume isn't the goal, it's the multiplier.
* The goal for Hypertrophy is proximity to failure (and increasing Mechanical Tension (load)). Ideally, reaching actual failure.
* The goal for Strength training is, well, lifting heavier weights.
* Neither of which rely on volume.
Volume does play a role, but only as a tool to help you achieve heavier weights, or more sets to failure. I only do about 4 sets to failure per muscle, per week and have still been getting significant results from it. My coach is having me run a program starting at 4 sets per muscle per week and that will undulate up to 16 sets to failure per muscle per week, then I will have a nearly 2 week deload to recover from it. I don't recommend this approach for you (or most folks here), but this is just to give you an idea of what the purpose of Volume is.
So I'm going to reframe training a bit.
* You have Main Work (Bench, Row, Overhead Press, Pull Ups, Squats, and Hinge (Deadlifts)).
* And then you have Accessory Work (literally everything else).
For your Main Work, are you adding 5lbs to every main lift - each time you train? Are you at least adding 5lbs per week per lift? If not, then I'd say you are putting in a lot of effort and not getting a lot of results from it (no offense, truly).
The goal of Phraks is to get your Main Lifts big and strong, and it is not a forever program. You should be adding 5lbs to every lift, every time you train... so less volume, but more progress.
Phraks Greyskull LP will be your Main Work, but you can still add Accessory Work such as Biceps, Abs, Pec Deck/Reverse Peck Deck, Forearms, Calves, Quads, Hams, etc. The thing with Accessory Work is that you can do as much of it as you want - so long as it is not interfering with the progress on your main work. So yes, Phraks may only take you 25 minutes in the gym - make sure you have >75% of your effort being put into those 3 lifts.
I also only recommend running Phraks until you don't see strength gains for 2-3 weeks (assuming Accessory Work has not interfered) in more than half your lifts. Really, you care about Squats, Bench, and Deadlifts - but you would do well to be strong in the rest of those lifts anyways.
Training does not need to change (and probably shouldn't change - dance with the girl you brought with ya) whether bulking or cutting, just give yourself extra leniency on lack of strength gains when cutting.