Is the husband's saying to his wife, "Do not go out with your friend (or else, upon divorce)" followed by his silence, considered a conditional oath?

This is neither a conditional nor an unconditional divorce, because the husband remained silent before uttering the condition for the divorce. Therefore, his statement does not result in divorce.

It is stated in "Fath al-Ali al-Malik fi al-Fatwa (definition) ala Madhhab (definition) al-Imam Malik": "What is your opinion regarding someone who intended to make his undivorced wife's divorce conditional upon her guardian not waiving part of her dowry, and he said: 'I swear by divorce, three [times],' but his father placed his hand over his mouth and prevented him from completing the statement, and then he consummated the marriage with her, and nothing of her dowry was waived?" I responded with the following text: "Praise be to Allah, and prayers and peace be upon our master Muhammad, the Messenger of Allah. No divorce occurred, and there is nothing against him, as our Imam Malik (may Allah be pleased with him) responded concerning someone who intended to make a triple divorce conditional upon something, and he said: 'I swear by divorce, three [times],' and then remained silent, as conveyed by Al-Mawwaq from Al-Mutayti from him."

The prescribed oath is to swear by Allah the Almighty. As for swearing by divorce, it is among the oaths of the dissolute, and one should be cautious of it.