What is the ruling on gesturing with a divorce accompanied by a slight sound, such as the Mauritanian expression "kat" (كط) or "maz" (مز)? And does this take the ruling of an explicit divorce if the husband does not intend divorce and gestured with his head in anger?

Pointing to divorce is not considered a divorce by the majority of scholars, but it is considered so by the Malikis if it is clearly understood. The mentioned utterance is not explicit in divorce, and an explicit divorce is that which contains the letters ṭā’, lām, and qāf (forming the word ṭalāq - divorce).

The mentioned sound is among the allusive expressions of divorce, and divorce is not necessitated by it unless intended by the husband. You mentioned that you did not intend it. Even if you had intended it, it would not be considered a divorce by the majority of scholars.