The rules are pretty clear, at least to me: only a roll with fear gives the GM a free spotlight for the roll.
Ok, the following is a) me thinking through how I understand the guidance of Daggerheart around the GM and Player "turns" and b) coming from the perspective of somebody who mostly runs games where the GM never rolls and everything comes from the player actions:
DH has the concept of a Player(s) Turn and GM's Turn. During the Player's Turn, one or more Characters are being spotlighted and acting. If at any time during that Turn, they meet any of the criteria previously noted (Roll with fear/Fail/Do something with stated consequences/provide a golden opportunity/look to the GM); the GM feels it's appropriate to make a Move; or the GM wants to actively intervene with a Fear action, they can do so.
One GM move is to Spotlight an Adversary. This allows for the standard array of Actions (Close move + act). The GM may also make a wide variety of other moves which, in the fiction, come from an Adversary. For instance, on a Failure with Hope, a couple brief examples given are "make them mark a stress from the adversary they're engaged with, or make an attack with them." The intent per p.100 is that in a situation involving battling adversaries, so long as the player characters are succeeding with Hope or Criting, those characters retain the spotlight, and the GM sticks to showing how the world and fictional situation is responding to their momentum (rolls should never leave the fiction the same). However in combat "someone fails a roll or rolls with Fear, or ... the GM spends a Fear to interrupt the players’ turns" is the trigger for the GM to take a full Turn, with includes "make[ing] a move to spotlight an adversary—and, if they wish, can spend any number of Fear to spotlight that many additional adversaries."
I'll note that on page 89 appears the single use of "the GM has the spotlight" I can find. I think that this should really be "on the GM's turn," because at least for me the intent is that characters (inclusive of adversaries) are spotlighted - not roles. Many things the GM is going to do will not involve spotlighting an NPC, but they'll absolutely be make moves and then spotlighting a PC by asking "what do you do?"