Does this qualify for 144 visa?

Under the assumption that you do not have any other stop within mainland China beside Shanghai, your itinerary is definitely eligible for 144 hour visa free transit and you do not need any kind of visa. Also, it is perfectly fine to have separate/unrelated tickets. I advise you to print out your flight tickets as well as your first accommodation booking confirmation for the first overnight in Bangkok to speed up the formalities upon your landing.