Is it permissible to supplicate and seek intercession with Allah by virtue of His love for the Prophet Muhammad (peace be upon him), such that the supplicant says: "O Allah, I ask You by Your love for the Prophet Muhammad (peace be upon him) to grant me such and such," and is this considered a forbidden intercession or shirk?

Scholars differ on the ruling of supplicating with "O Allah, I ask You by Your love for the Prophet Muhammad, peace and blessings be upon him":

The first opinion: It is a permissible form of tawassul (seeking nearness to Allah through an intermediary), and it is considered tawassul through one of Allah's attributes. It is legislated, like tawassul through Allah's knowledge and power, as in the Istikhara supplication.

The second opinion: It is not explicitly reported and is not among tawassul through Allah's names and attributes. Sheikh al-Islam Ibn Taymiyyah mentioned that asking "by the right of so-and-so" or "by the status of so-and-so" is not a cause for the supplication to be answered, unless there is a supplication or intercession from them, or a cause from the supplicant, such as his obedience and adherence to them. Thus, tawassul through the servant's love for the Prophet and his obedience to him is a great cause for the supplication to be answered.

In conclusion, this phrasing is ambiguous, and it is better to leave what is doubtful for what is not doubtful. Tawassul through the supplicant's love for the Prophet, peace and blessings be upon him, is tawassul through his righteous deed, and it is legislated without dispute.