Stone Golems cannot breathe.
PCs turned into Stone Golems cannot breathe.
The Polymorph spell can only turn creatures into beasts, a PC can't be turned into a Stone golem with Polymorph and a petrified PC is not a stone Golem, it is a PC with the petrified condition. If such petrified PC is then polymorphed into an elephant, or mouse or horse or snake, then it becomes a petrified elephant, mouse, horse or snake for the duration of the polymorph. If the petrification ends before the polymorph it becomes a non-petrified elephant, mouse, horse or snake.
Does a PC turned into a Stone Golem die of suffocation?
You would need True Polymorph for this, which is a 9th level spell and the answer is no because it would not be a Human or Dwarf or Elf or whatever it would be a Stone Golem while polymorphed and would not need to breathe.
This is not the same as being petrified. A petrified Human or Dwarf or Elf is still a Human or Dwarf or Elf and needs to breathe. RAW they can breathe since the petrified condition does not prevent breathing, it only prevents actions and moving.
You know what else doesn't need to breathe? A statue.
True Polymorph could also turn a petrified PC into a statue (it could turn a PC into a statue whether the PC is petrified or not). While the PC is a statue it would not be petrified, because petrified is a condition that applies to creatures.
Petrified people don't suffocate because they don't have to breathe.
In D&D 5E RAW petrified creatures don't suffacuate because they can breath. Petrificaiton does not prevent breathing. Further a petrified PC is not a statue.
(TECHNICALLY Stone Golems don't have a 'no breathing' trait, but its implied)
Yes they do, it is covered in the rules it is in the monster manual on page 167:
"Constructed Nature. A golem doesn’t require air, food, drink, or sleep." but a petrified PC is not a Stone Golem.