Are one-shoulder, sling backpacks authorized in Navy uniform?

Yes these backpacks are authorized. Ch.2 Uniform Navy Regulation. Quote "All bags worn with the uniform must conceal its contents and be either solid black or navy blue in color. There will be no personal ornamentation attached on or to the bag. Computer bag/brief case and backpacks: may be worn across the left shoulder of the Tropical Blue or Winter Dress Blue uniform to facilitate saluting. When wearing a bag, the strap must be worn across the left shoulder (fore and aft) with the bag hanging on the same side of the body. The case or bag will not be worn with the strap and bag on the opposite sides of the body (diagonally). Backpacks may also be worn over both shoulders when wearing the ODU.

"The case or bag will not be worn with the strap and bag on the opposite sides of the body (diagonally)."

This would mean that bag is unauthorized if you wear it as intended (cross body)

It says the strap and bag must be on the same side on the body. So as long as you don't have it slung across your body, you should be fine.