The following sentence is from the book コンビニ人間:
My question is: what is the role of と here? How would the meaning change if this と were omitted? I can't seem to find any grammar point on this usage.
have the exact same meaning. と can be stuck to the end of certain adverbs （ゆっくりと、黙々と、次々と、のんびりと etc）. Depending on the usage it can make the sentence sound slightly more formal / higher register or place slightly more emphasis on the adverb in question, but ultimately has no real effect on the actual meaning of the sentence.
Hi and welcome to JPStackexchange!
だんだんと is "an expression that means that the degree of something changes or progresses gradually, little by little, in order. An adverb that modifies a verb."
CollinsDictionary translates だんだんと as "slowly" and だんだん as "gradually, increasingly", so I think だんだんと is not as strong in the gradual increase.
(Nice book recommendation by the way!)