Three nights in Shanghai, then 2 nights HKG, then 4 nights Taiwan - - 144 hour exemption eligible?

We are both American citizens. We will fly from Moscow to Shanghai on China Eastern (departing Oct 13, arriving the morning of Oct 14), stay in Shanghai for three nights (Oct 14, 15 and 16). Then we fly (again on China Eastern) from Shanghai to Hong Kong on Oct 17 and stay two nights (Oct 17 and Oct 18). Then we fly (on China Airlines) from Hong Kong to Taipei on Oct 19 and stay for four nights (Oct 19, 20, 21, 22). Then we fly(again on China Airlines) from Taipei to Osaka on Oct 23. We have confirmed flights and confirmed seats for each of these segments. We do not return to China nor Hong Kong nor Taiwan after this.

Is there any bearing of the travel to Hong Kong or Taiwan that could impact our eligibility for the 144 hour free transit exemption?

Thank you.