TAIWAN-SHANGHAI-HONG KONG

Im not really sure how the 144h free transit works.
I was supposed to fly from Taiwan to Shanghai, stay there 150h and then fly from Shanghai to Poland.
I noticed however that applying for a Chinese visa in Taiwan would be very costly for me, anyway I dont want to go back to Poland anymore.
I was planning on cancelling my plane back to Poland and instead booking another flight to Hong Kong so that I would not exceed the 144h.
Does it however classify as a transit flight? I would probably fly with the same airline but obviously not on the same ship. Does it have to be written that it is a transit flight or do I just have to show that I have another ticket to a third country?