The passages are split between the story of David coming to power and a hall of fame listing of David's mighty men.
An Amalekite finds David to report Saul's death. He even brings the crown and royal armband as proof. This is different from the account in 1 Samuel 31:1-7 where Saul takes his own life. My commentary suggests the Amalekite may have come across Saul's body and looted it before the Philistines were able. His report to David was intended to gain favour in the eyes of the new king. A grave miscalculation. David had him cut down without ceremony for destroying the Lord's anointed. This is consistent with David's character, who repeatedly refused to take advantage of situations and harm Saul.
One thing that stood out to me later in the narrative is how David did not have the throne handed to him after Saul's death. He was first anointed king of Judah before going to war with Saul's successor. David was king in Judah for seven and half years! It makes me think of the saying "when God closes a door, He opens a window." I have often thought the statement trite. The Bible is filled with stories where someone must stay the course and have faith before ultimately being rewarded with what had been promised. A faithful life is not about finding a convenient or most efficient path. Sometimes we need faith that the door will burst open with our continued efforts and in God's time. Our faith and character will be increased because of the experience.
I wonder about how the mighty men on these lists are grouped. The lists are not identical and the order is different between the lists in 2 Samuel and 1 Chronicles but notice that there are a some parallels, including a specific group of three listed at the forefront. Jesus had a group of followers, yet limited His close contacts to the disciples and His inner circle to just three. Could the mighty men have similar structure? It may be worth a deeper dive or could end up being a rabbit hole, but could be interesting nonetheless.