I have bought lots of new motorcycles and I do check out the manufacturing date on the tires. Typically I see tires that are between one and two years old. That makes sense. The motorcycle manufacturers have to have tires shipped to them from the factory, which may take several months being packed into a container, shipping to the dock, waiting on the dock for a ship, time on the ocean, time at the receiving dock and customs inspection, truck shipping to the motorcycle factory, off loading into the factory tire storage room, where they sit for a while waiting to be mounted to a new motorcycle. Then it may take six or more months for the motorcycle to be shipped across an ocean (see above), then to the distributor's warehouse, inventoried, ordered by the dealer, shipped by truck to the retailer, sitting on the showroom floor before being sold to the customer. That can take a long time and the tires age accordingly.
On the other hand, you would expect that a tire that you order from an on-line accessory company would be fresher. That is usually the case, but not always. When I order a sport-touring tire from a company like Motorcycle Superstore or Revzilla, I typically see a tire manufacturing date between six months and a year old, but a less popular tire, such as a Zero or my Triumph might use, might be much older. Sometimes, but rarely, I have received tires that are almost three years old.