Is supplicating to other than God, such as saying "By the Prophet, I implore you to visit me," considered an oath by other than God, taking into account the verse from Surah An-Nisa: "And fear Allah, through Whom you ask one another, and the wombs," and the story of Utbah ibn Rabi'ah?

Swearing by other than Allah is forbidden according to the majority of scholars. This is the view of Abu Hanifa and one of the two opinions in the Maliki and Hanbali schools, and a consensus of the Companions has been reported on this matter. As for seeking intercession through the Prophet's (peace be upon him) status (jah), it is not permissible. The verse from Surat An-Nisa: "And fear Allah, through Whom you ask one another, and the wombs," has been interpreted as an command to fear Allah and maintain kinship ties, or as an oath by Allah upon the wombs, and Allah has the right to swear by whatever He wills. The statement of Utbah ibn Rabi'ah indicates that swearing by kinship was a custom among the Arabs before Islam.