Beyoncé and Chris Martin have been friends for years. Still, she wanted no part of a song he tried to give to her.

It was around then that they truly felt the drop, beginning a decades-long free fall in which songs have appeared to Chris Martin from some enigmatic source to be shaped into hit Coldplay records.

Before performing “Everglow,” the British rock star invited a Pakistani fan onstage and mentioned several crises around the ...