What title did Qing China use for US presidents?
Formally, the Chinese title was President - that is, the English word President was transliterated into Chinese as 伯理璽天德. From the Treaty of Wanghia (望廈條約):

以上關涉太平、和好、貿易、海面各款條約，應候各大臣奏明大清大皇帝批准，大合眾國大伯理璽天德既得各國選舉國會長公會大臣議定允肯批准...
The present Treaty of peace, amity, and commerce, shall be ratified and approved by the President of the United States, by and with the advice and consent of the Senate thereof, and by the August Sovereign of the Ta Tsing Empire...