I'm sort of a beginner to weight training. Often I find I can't fit in everything I want to do in my workouts given my time constraints - I can work out at most 5 times a week for about 1.5 hours, and I want to hit chest/arms/shoulders/back twice per week, and legs once per week (maybe twice if I can fit it in). Typically I do chest/arms on one day, then back/shoulders, then legs.
I typically start with chest, and by the time I get to arms, my triceps are exhausted, and I'd need a much longer break than is practical to move the same weight around as I normally could. For instance, when I'm well rested I can do 4 sets of 12 dumbbell skullcrushers with 25lbs, but after chest I can only do 4 sets of 6-8 with 22.5lbs.
Recently, I started doing sets "whenever I feel like I have the energy." I have a dumbbell set at home, so whenever I'm bored I'll do 4x12 dumbbell skullcrushers, or 4x12 dumbbell concentration curls with 30lbs, or 4x10 dumbbell shoulder presses with 50lb dumbbells, etc. The point is that these numbers are often astronomically better than what I can put out in the gym after the first half of my workout. I feel like I'm limiting my capacity for growth doing 4x8 skullcrushers with 22.5lbs when I know I could be doing 4x12 with 25lbs.
Is there just as much benefit to doing exercises "at random times throughout the day" as there is to doing them all in a single workout? Part of me thinks "it all counts as volume, what's the difference between whether I do this in the gym at a scheduled time, or at home throughout the day?" Another part of me thinks something is "wrong" about this approach - my gut says it wouldn't be as effective to do 5 different exercises spaced out over a 12 hour day as it would be to do those same 5 exercises in an hour window. Perhaps something about the shorter rest times contributes to greater muscle damage/hypertrophy. Is my gut right or wrong?
If there truly is no benefit doing exercises at "random times throughout the day", and I'm just wasting my time, then what can I do as a beginner to increase my weekly volume without dramatically increasing my rest times/workout lengths? Should I just do each of chest/arms/shoulders/back once a week on a separate day, so that I can push the most amount of weight on each day? I wish I could do two muscle groups on a single day, but my body just isn't ready for that kind of fatigue I guess.