I would hazard there isn't any "authentic" style, but rather a whole lot of them, as varied as the hunter-gatherers and primitive farmers we know about historically, but probably considerably more advanced than those whose lifestyles survived to the present (because those that outgrew the stone age were sophisticated enough to presage the age of metalworking, and here we are today).
Our stone-age ancestors weren't dumb, and certainly were creative in the same ways modern humans are. And as you say very little preserves that wasn't stone, but it stands to reason anything available that could be worked by hand got used. Neanderthal camps have revealed that they had birch-sap glue and little portable oil lamps, and lately there was discovered the remains of a shaped-log cabin that had been preserved because it had partially burned. (I have long contended that we have so little of their tech because they used a great deal of wood.)
I expect stone-age lives were full of objects made from wood, fiber, leather, and other animal products that didn't preserve, and that pretty much anything you can make (or decorate) without a gas-fired forge is fair game. Otzi was stone age, but he was not a primitive.
And there's evidently a lot of interest beyond our little corner of the internet. "Primitive Technology" on Youtube has over 10 million subscribers. He makes all sorts of stuff starting with just himself and whatever he can find in the wild. (My favorite was the brick tiny-house with a tile roof, fireplace, and a sort of hypocaust, but he's also made little iron knives from rust bacteria found in streambeds. Gonna be some puzzled future-archeologists.)
I quite like your stone-age garments and toolkit. Looks functional, comfortable, and useful, what more do you want?