Is the husband's saying to his wife, "I cannot continue like this," and her saying, "Nor can I continue," considered among the allusions to divorce, and what is the jurisprudential basis for divorce by allusion?

What happened does not result in divorce, because you did not utter an explicit divorce nor did you intend it. The original state is the continuation of the marriage, and it is not nullified by doubt. Divorce by كناية (allusive term) occurs if the man intends to effect a divorce and utters a word that could bear that meaning, for words are meant to indicate the intentions of their speaker. We advise caution against excessive questioning and delving into the intricate details of divorce matters, as this opens the door to obsessive doubts (وساوس).