Kind of 2 suggestions in one, it would be nice for luck to affect errands. Characters with higher luck have a better chance of bringing back one of the drops listed.
Adding character specific bonus would also be nice as well. I’ll use HSR/Genshin as an example here because they have a similar errand system (it just takes longer depending on how long you send them out) but I’m sure other gachas have similar mechanic. Currently on HSR if you send someone out for an “errand” there’s a recommended path, and if the character matches that path they bring back bonus material. Non matching characters still bring back the base amount but bring no extras.
For a LW example, if I sent out an errand for foraging mushrooms, if I send out Marisa or anyone with a “forest” tag she should get a bonus to bring back extra materials OR a chance to bring back extra materials. You can see here the quest is for wood, so she can have a chance to bring back more woods. If there was a cube errand, she could have a higher chance of bringing back a cube because those are not guaranteed. Same would go with other errands, if there is a shrine maiden/shrine festival errand, then shrine maiden tags or religious tags could get a bonus