Genshin headcanons:
Paimon is a mini coin bank. Sometimes she would take few mora out of chests and hide it in her mini pockets. In that way when they are a little short on mora, she can take some from her pocket and give it to the traveller
Diluc reminds the workers around the Dawn winery to frequently leave apples around in case the traveller swings by.
Amber always checks the missing posters to see if they are damaged by the rain so she can replace it with a new one. This includes those posters in hidden places such as the back of the knights headquarters and those above the windmills.
Being an adventurous chef, Xiangling frequently runs into the traveller in her travels. They would share meals before she goes back to Liyue and would leave some extra supplies for them to take.
Klee would sometimes purposefully escape her room so that Jean would be taken away from working too much. She gets tons of sweets from Lisa and Kaeya for that!
Zhongli would go share meals with Cloud Retainer and most of those times are spent talking about Xiao, Ganyu, and Shenhe.
Whenever they go around Watatsumi, Traveller would leave flowers on Teppei's house, on the spot where they last saw him.
