There is an old coaching truism that the team takes on the personality of the coach. This is true at a general technical level. Coaches spend more time working on things that are important to them, and so after some time, the team will take on some of those characteristics.
It is also true at a less obvious internal level. If you want to have a calm, resilient team of problem solvers, that is the way you have to act. If you want to have a team of emotional, fighters that is the way you have to act.
It is absolutely true at a daily working level. The team very quickly and intuitively picks up on the mood of the coach. If the coach is angry and surly, the team will be quiet to avoid unnecessarily antagonising them. If the coach is happy and relaxed, the team will be relaxed. If the coach is very serious and workmanlike, the team will also be serious.
The lesson is that the coach has the capacity to create the daily working environment that they want. When the team needs to be looser, be loose. When the team needs to be more focused, be focused. And sometimes it is okay if everyone walks on eggshells for a day or two.
You are the coach, set the mood you want.