Don't get riled up about this. Countries do that out of diplomatic courtesy all the time. There is nothing degrading or subservient about it.
Asking another country to pass a message is not the same as telling the country how to act. The country receiving the message fully understand it is from the originating country and not the position of the courier country.
The message can be written or verbal. If the message is verbal and insulting or threatening to the receiving country, the courier country can always reject it.
Proper diplomatic courtesy between two antagonising powers in the face of incompatible political agendas, let alone during normal course of diplomacy, would be the 'exchanging of views' where either side lays out their positions and, if the US side so chooses, to express to the Chinese side their viewpoints and concerns vis-a-vis China and Russia... and their 'expectations' from either party, if the US side wishes to be so bold.
Yang, for his part is of course well within rights to take everything Sullivan says 'under advisement'. Sullivan can make requests and demands all he wants, just like Yang can vice versa.
What is
not appropriate (not suggesting that's actually what had happened, as we simply don't know) is the diplomatic faux pas of the US expecting China to relay at the leadership level communique not meant for Chinese leadership, but the head of state of another country.
This is essentially Jake Sullivan,
National Security Advisor, senior aide and assistant to the Executive Office of the President of the United States, "asking" Xi Jinping,
President of the People's Republic of China and General Secretary of the Communist Party of China, to pass a note to Vladimir Vladimirovich Putin,
President of the Russian Federation and Commander-in-Chief of the Russian Armed Forces, effectively reducing this affair to one where
the leader of China mediates between the US President's aide and the leader of Russia. So yes, this would be absolutely degrading and wholly against diplomatic protocol.
This isn't the first time the Yanks have pulled this stunt. Remember when Lloyd Austin requested repeatedly for months to meet with Xu Qiliang, head of the Central Military Commission, and was denied repeatedly?
Proper protocol for the US Secretary of Defense is to deal with his actual counterpart, the Minister of National Defence i.e. Wei Fenghe, not the higher-ranking Chairman of the CMC (or rather Vice-Chairman since the Chairman is Xi Jinping) whose counterpart is the Chairman of the Joint Chiefs.
All of Austin's predecessors had followed this most basic norm, but not my man Lloyd. So against protocol, he naturally had the door soundly shut in his face -
And who did he get to speak with finally? Minister/General Wei after all -
And who did he get to met at the Shangri-La forum? Minister/General Wei -