The calls were not the real 贸易谈判, they were

calls to propose going back to trade talks.

One of the calls was likely from Liu He to Trump's team, because Liu disclosed that info himself. The other call Trump didn't want to reveal would be likely from Xi, because Trump won't take calls from lower level officials from China.

Another intention of the calls from China obviously was that China tried to use these calls to hold Trump up or distract him from forming close allies with other countries in G7 meeting.   Why so urgent? They knew Trump was there, not in WH.