[ If Zhongli takes notice of Childe's blush, he does not say anything but nor does he seem interested in pulling back from the other. Or not too far at least as he reaches for the bath salts next to liberally sprinkle into the water. He seems appeased, no that is not quite strong enough word for it - excited by Childe's answer and presence. Continued presence if Childe is hinting that he will be allowed to stay for at least a few days.

Zhongli had no expectations for what would happen after he found Childe again = only contingency plans for if he was turned away (and those half-forgotten most of the time). So to be here and to be allowed here for a while longer, finally the fluttering uneasiness in his chest had quieted to a contented hum. Finally he was feeling a sense of peace which had been eluding him for months if not years now. ]

Then might I impose you to direct me to the markets later so that I may make some purchases.

It will also give me something to pass the time while you are busy with your own duties.

[ Because it wasn't like Zhongli expected Childe to drop everything and take care of him. He wasn't an invalid - just forgetful. And with the right precautions and muscle memory to guide him, he should be able to co-exist in a way that would not burden Childe's day-to-day. (Burdening Childe's heart and mind was a different matter entirely.) ]