Do I need a China visa for Taiwan? China flights with Japan, which are booked with different airlines?

We are Americans and fly this route:

  1. USA> TPE
  2. TPE> PEK
  3. PEK> KIX (5 days in Beijing)
  4. Train to Tokyo
  5. NRT> USA

1 and 2 are on the airline A, 3 on the airline B, 5 on the airline C.

I assume that airlines do not matter, only the Chinese cities, so for a 144-hour visa.

Source: https://www.travelchinaguide.com/tour/visa/free-transit-144-hours.htm

Related topics: What does "Confirmed Seat" mean in relation to the 144-hour visa-free transit from Beijing?