Multiple 144 Visa Free Transits?

I’m American with a US passport traveling from US ultimately to Viet Nam then back to US via Shanghai. I intend to use a rewards ticket (round trip) with a US carrier for 1st part of the trip, US to Shanghai. I’d like to layover a few days in the Shanghai region if possible, then use a separate booking (Shanghai to Ho Chi Minh city) purchased prior to leaving the US to travel to Viet Nam. My return would be the reverse. Hanoi to Shanghai on a separate booking, stay a few days in Shanghai, then return to US on the return leg of my rewards ticket with original US carrier.

Can I benefit from the 144 hour free transit, or would i need a regular mainland China visa? I’d like to stop over in Shanghai for short periods of time while avoiding the $140 USD regular entry permit expense. In other words, does a separate trip to/from Viet Nam from/to Shanghai create 2 separate trips?

Thank you in advance.