Does the sentence contain a pronoun agreement error? After anyone eats Yzma's famous chili, they swear to never try another kind.

Yes.  There is an agreement error between 'anyone' (a singular pronoun) and 'their'  (a plural pronoun).

Explanation:

Some ways to fix the error

After anyone eats Yzma's famous chili, he or she swears to never try another kind.

OR

After people eat Yzma's famous chili, they swear to never try another kind.

By the way, there is another error in the sentence

NO:   'to never try'

YES:   'never to try'

true. the definition explains it: a word or phrase that modifies or qualifies an adjective, verb, or other adverb or a word group, expressing a relation of place, time, circumstance, manner, cause, degree, etc. this is a dictionary definition that i have looked up in a dictionary.

the author wants to draw the reader deeper into the experiences.