Am I eligible for 144 Hour Visa Free if I book 2 roundtrips, with Shanghai in the middle?

Hello, does the below work out:

Roundtrip Ticket 1: NYC > Shanghai (5/16/24 - 6/1/24)
**144 Hours: Will enter Shanghai 5/17, since this policy starts the next day..thinking I could stay 5/18-5/23 in the city. Before 5/23 ends, I will be leaving.
Roundtrip Ticket 2: Shanghai > Astana (5/23/24 - 6/1/24)

I plan to enter Shanghai for ~5-6 days from USA, and then leave for Astana (Kazakhstan) for a business trip. Once the trip is over, I plan to return back to Shanghai in time for my flight back to USA on 6/1/24 (I will not be leaving Shanghai Pudong Airport, simply returning to Shanghai so I can return home).

Also, my Roundtrip 2 may contain a stop in either Xian/Urumqi to transfer flights to Astana (not leaving airport)...those are the only options I see available for my specific dates above.

Booking 2 roundtrips here instead of various one-way tickets because I find it more affordable. Please let me know if I am eligible. Thank you!