Ahh, this is a cute idea! I'm imagining Zhongli and Alhaitham having a long standing pen pal arrangement discussing linguistics and history, but recently they've had an unsolvable argument over some ancient Liyuean dialect. Zhongli, feeling the need to prove he's correct and with plenty of time in his hands in retirement, decides to take some invaluable ancient text to Sumeru to validate his argument. Not realizing this penpal is the acting grand sage.

Childe is just dragged along for the ride (hmm, perhaps after the recent Fatui-incident he should even be in disguise? Maybe as a toyseller 😂). I'm filing this idea away for later!