One of the fun nuances of the world is that different regions often have different sayings depending on their culture or history. These little sayings and phrases give insight into the type of people that live there, and in some cases can do a lot to both ground someone in the culture of what is going on in that area, and express differences between two places.
Coming up with these sayings can be hard. At the same time, you can always just steal them from the real world and apply them where they fit. Be mindful of that you do this respectfully, but as long as it is for a private game you mostly only need to worry about not insulting your group - as much as it's best to just treat everyone with respect whether you're being overheard or not.
What do I mean by this? Well consider. In the United States there is the saying "The squeaky wheel gets the grease." This effectively boils down to you have to make yourself noticed to get what you want. If something is wrong, complain and it can be fixed. But it can also be used just to express that it is the thing that stands out that gets the desired result.
Japan however has a different saying. "The nail that sticks out gets hammered." Which is kind of the opposite in meaning of the United States saying. Both involve a problem being noticed and resolved, but the connotation and usage are very different.
These sayings help highlight that the United States has a very individualistic culture where you as the individual are supposed to stand out. It's why we have phrases like "I'm not my job" and other things. Whereas Japan has a lot stronger of a group culture, where how you fit into the group and what you belong to is considered more important than who you are as an individual.
Those are both super simple takes on the traditional culture of both. The U.S. is not free of any group think (in fact, modern complaints are you have too much in some cases.) Japan is also not a stranger to individualism. But where their culture emphasizes the importance is different.
Hinting At Something More
You can also use these sayings and idioms to hint at aspects of the setting. In one of my D&D games the PCs found an isolated village that had common sayings that all ended "or the fairies will take you." This basically boiled down to advice like not being up all night, not leaving the village all night, and making sure to secure your home at night. It seemed like a cute enough thing to the players that just added charm to the village...until people who were out at night were abducted by faeries.
Very on the nose, but at the same time in a fantasy world like D&D warnings about the supernatural taking you away (as many nursery rhymes do) are just a little bit more real. And as a GM you can lean into that in a lot of fun ways.