In external Chinese diplomacy, Hong was no diplomat nor could he see that the Western Imperialist governments would be very sympathetic to a Chinese rebellion – they expected the new government to recognize Western rights in the Colonies already held. With his dealings with western nations, Hong often treated the ambassadors as inferior dependencies in the same manner as the Manchu government tried to deal with the British before the Opium Wars. If say Hong was willing to part with the whole of Guangdong and Fujian provinces, which technically were not under his direct control, the British and Americans and others would be all too helpful to aid in his victory – not only recognizing the Heavenly Kingdom as the new Chinese government, send money and supplies, but would see the quick defection of Charles George Gordon, Frederick Townsend Ward, and Henry Andres Burgevine to support the rebellion militarily. Unfortunately, due to the Heavenly King treatment of Britain and the British, Sir George Bongham, the British plenipotentiary in China, left in disgust threatening that if British lives or property were violated that his government would retaliate with acts worse than they did back in the Opium Wars.
But let us say the rebellion was successful...
I suspect that Hong's nation would be much like ISIS / ISIL / Al-Qaeda state. It will likely treat its neighbor like a ISIS / ISIL / Al-Qaeda state did in IRL. Japan would look towards the Manchu as they did post-World War One, as the rightful government and would install a Puyi style puppet by force. Korea might do the same, but also expect a purge of Christians.