Exergonic vs Endergonic Reactions Problem
Problem 3, concept check 8.2 from Campbell Biology [1, p. 150]:

Some partygoers wear glow-in-the-dark necklaces that start glowing once they are “activated” by snapping the necklace. This allows two chemicals to react and emit light in the form of chemiluminescence. Is the reaction exergonic or endergonic? Explain.

Answer
Answer key [1, p. A-8]:

The reaction is exergonic because it releases energy—in this case, in the form of light. (This is a nonbiological version of the bioluminescence seen in Figure 8.1.)

From [1, p. 143]:


Figure 8.1 The green glowing spots on the outside of this Brazilian termite mound are larvae of the click beetle, Pyrophorus nyctophanus. These larvae convert the energy stored in organic molecules to light, a process called bioluminescence, which attracts termites that the larvae eat. Bioluminescence and other metabolic activities in a cell are energy transformations that are subject to physical laws.

Question
The answer is an exergonic reaction. What I understand of an exergonic reaction is that not only does it have a negative $ΔG,$ it releases energy. In this case, the energy released is light energy.
My original answer endergonic reaction as for the problem given, to “activate” the necklace, doesn’t it require energy from partygoers to snap the necklace? Is the $ΔG$ value for the light being released much less than the $ΔG$ value of the energy being used to snap the necklace?
Reference

Urry, L. A.; Cain, M. L.; Wasserman, S. A.; Minorsky, P. V.; Orr, R. B.; Campbell, N. A. Campbell Biology, 12th ed.; Pearson: New York, NY, 2020. ISBN 978-0-13-518874-3.
The reaction to consider is the transformation of chemical energy into visible radiation (light) and a little of heat.  A glowing stick consists of at least two compartments which -- on purchase -- a supposed to be kept separate.  The snap only breaks the wall between the two so that chemicals may mix with each other to start chemoluminescence (work principle), a principle similar to a firefly in late summer, too.
To decide if the reaction is exothermic, endothermic; exergonic or endergonic you have to compare the energy of initial state (when the chemicals are separated, no emission of light) with the one after the reaction.  There may be an energetic barrier to trigger the reaction, equally known as activation energy, but in its current form, this detail is not relevant to answer the question.
Take an analogy employing potential energy you might recall from the physics lecture: imagine you ate in a restaurant on a mountain and now walk back home.  It is not relevant that some energy was required to get up from the table, it is only about the comparison between
$$\mbox{state A «being in the restaurant»} \ce{-&gt;} \mbox{state B «back in the valley» } + \mbox{energy}$$
Even the pathway, straight downhill, or passing some smaller hills to reach the destination is not important here.  The naming then is, by convention, a formalism.