The Knicks need a longer term solution at Point Guard. Neither Burks nor Noel represent long term pieces of their team. They trade them get three years with Brogdon, and give up an extra first for the upgrade.
The Spurs have extra cap space, and use it to swap Richardson for Graham, who, despite their reputations, have similar statistical profiles, and get a backup center as well, receiving 2 second round picks as compensation for the cap space.
The Pelicans clear some 2023-2024 space for when Williamson's contract extension kicks in. They give up the potential of Hayes in order to do so, but they have a roster filled with young players, and with Nance and Valanciunas and the return of Williamson, his presence represents a luxury. They have a surplus of picks, so giving up 2 seconds doesn't hurt, since they have only 1 open roster spot anyway, they don't have room for 3 picks this year. They also have the #8 pick, who will need minutes this year. They also upsize their backup backcourt, with the rest of it being made up by the undersized Alvarado and Lewis Jr.
The Pacers receive a 2023 first round pick, which has the potential to be a lottery pick, a young big to potentially grow into a long-term backup, or even replacement for Turner. Garret Temple is really just cap filler, but with Brogdon and (presumably) Rubio leaving, some veteran presence in the backcourt would be helpful. They also need to have minutes for their 6th pick, so removing the most expensive piece of their backcourt with the longest contract makes sense.