Peter would likely throw himself into being Spider - Man even more. By helping others and fighting crime, he distracts himself from his own pain. He sees it as his duty to protect the city, especially in the post - Infinity War chaos. This gives him a sense of purpose and helps him focus on something other than his own trauma. He believes that if he can make a difference, it will somehow make up for the losses he's suffered.
He also copes by relying on his friends and family. Aunt May, for instance, would be there to support him. She would offer him a home, love, and stability. And his friends like Ned would be there to have his back, to talk to him about his feelings. Together, they form a support network that helps Peter deal with the trauma of the events he's been through.
Peter Parker might cope with trauma by using his sense of humor. It's something he's always done, even in the face of danger. In the aftermath of Infinity War, when things are really tough, he could use his jokes as a defense mechanism. It helps him keep his spirits up and also makes those around him feel a bit better.