Taiwan-SH-NJ-SH-HK 2024

Under the assumption that you have mentioned your all stops within your itinerary, you are definitely eligible for 144 hour visa free transit in wider Shanghai area and you do not need any kind of visa.

Your planned travel to, I assume Nanjing is perfectly fine because Nanjing is located within Jiangsu province and consequently allowed to travel to within this 144 hour visa free transit scheme. Here just one suggestion... If you can, you could take a flight to Shanghai Hongqiao airport because this airport is practically next to Hongqiao station of high speed trains. However, if you cannot or the flights are more expensive, than Pudong will do the job as well.

After your flight to Hong Kong, there is no need to bother with the following step because this is a detail of no particular interest to mainland Chinese authorities.