Is the husband's saying "I will forsake you," and his interpretation of it as "I will leave you, or distance myself from you, or quarrel with you," considered a divorce or a metaphor for it?

The words mentioned are neither an explicit divorce nor an implicit one. Rather, they are a promise of abandonment or distance, so no divorce takes place by them. It is not incumbent upon the woman to question her husband about every word that might carry the meaning of divorce.