How to make professional style burger buns?

The stretch and fold method is great for making breads, but most buns like this are made using something closer to the Chorleywood Process (or No Time method). Instead of resting time with stretches and folds and bulk fermentation time, this method relies on combinations of dough conditioners and heavy mechanical mixing. This usually means that the dough is mixed with a relaxer such as l-cysteine and an oxidizer like ascorbic acid. The dough is fully developed mechanically and shaped immediately, then proofed and baked.

This will be very hard to achieve at home primarily due to the conditioners used. L-cysteine and it's precursor, glutathione, are both extremely potent. A batch of hundreds of pounds of dough may require less than an ounce of conditioner, so it would be virtually impossible to scale this at home. You may be able to achieve similar results using a deactivated yeast, such as brewer's yeast, or by deactivating yeast on your own. The results will be slightly different though, as the amino acid profiles will be different.

Equipment used in a professional bakery will also make an identical result harder to obtain. Bakeries use enormous mixers that can provide more power than a home mixer, as well as special pans to help hold the shape of the bun as it proofs. Professional ovens also allow much more precise control of air flow and moisture retention than a home oven.

You may be able to achieve a good enough result with an enriched dough (like challah) and some tweaking, but it will be very hard to make an identical bun.