Formula may help him to sleep longer. It does this because of three reasons
i) the bottle giver tends to be 'in charge' of the amount given, encouraging and offering and coercing a bit more into the baby when the baby might 'switch off'
ii) the baby may suck and swallow because that's what 'sucky' babies do, for the pleasure of sucking. Breastfed babies do this, but the milk supply and flow is responsive to their suck in a way that a teat and bottle isn't - bottle fed babies tend to take more in volume as a result which is one of the reasons they tend to be larger than breastfeds after the first 5-6 months
iii) formula milk takes longer to metabolise than breastmilk
None of these reasons work in line with the baby's physiology.
Maybe your baby does wake up because he is hungry in the night - hard to tell. But there is nothing nutritionally wrong with this - he's hungry, he wakes, you feed him, he grows and thrives!
Maybe he is waking just 'cos he is still only 3.5 months old and plenty of babies do this whether they are breastfed or formula fed. It's what some babies do.
It's up to you to decide if you want to give formula (which may or may not work) or to work on other ways of having a less disturbed night, or otherwise more sleep. Your well-being is important, too.
Your tiredness is unlikely to affect your supply - maybe your baby needs feeding more in the night and in the day because of his particular needs at that time, not because of a drop in supply. Whatever - I can understand you need to feel better about all of this and to feel somehow more rested.
But nothing you are doing is wrong, and there is nothing wrong with your milk or your feeding.
If you supplement, you need to know why you are doing it, that's all - and it's not because there is something lacking in your milk or your feeding