My approach:
1. Put a reasonable amount in savings first, but make sure to leave yourself enough to enjoy life, because you can't be completely sure you'll be alive in 1, 5, 10 or 20 years.
2. Spent on monthly expenses without stressing about savings, because some fun money is also part of your budget.
3. If there's any money left over when you get your next paycheck, send that into savings as well.
If buying a PS5 is really important to you, then by setting money aside for it you are paying yourself first. For most working people, though, there are much more important things to save for, and the wiser decision would be not to buy the PS5 if it means reducing the savings.
If you instead allocate first, and operate the month assuming you never add had access to the funds, then it becomes painfully obvious that you've spent beyond the target -- and can make the decision then whether that's fine, and pull out the money from the savings buffer as needed (and presumably up the savings envelope for next month).
The main thing, I think, is that most people (not living hand-to-mouth) spend to their financial comfort -- not their physical comfort -- growing concerned mainly as they approach their upper limits, and then reduce accordingly. I'm thinking of Braess's paradox; you spend to the money you have, even if you'd be happy & fine with less.
So by reducing the total funds up front, you reduce spending earlier accordingly. Of course, no more so than what would make your lifestyle uncomfortable.
Also a mental bias against spending is not necessarily a good thing. Spending is like eating, unless you have a problem where you're doing it too much of it, doing less of it is not inherently desirable. I spent way less last year than 2019 because of Covid and my life certainly wasn't any better for it.
Which is significantly better than the other way around, because you’ve met your saving target(s). Really, that money constitutes legitimate excess cash. You can shove it into risky investments, or spend it freely; it doesn’t matter — you’ve met your needs.
> Also a mental bias against spending is not necessarily a good thing. Spending is like eating, unless you have a problem where you're doing it too much of it, doing less of it is not inherently desirable
If you’re spending over your saving targets, you are spending too much. If you’re spending under your targets, you’re free to spend more, guilt-free (you’ve covered your necessities, you’re playing with excess).
The only problem is if you set your savings budget so high that you can’t spend to your actual comfort (given your lifestyle). Then it becomes a question of accepting you simply don’t have so much money, and either reduce your lifestyle or extend your saving targets accordingly.
TLDR; meet your targets. Beyond that, do as you wish.