Is praying upon the Prophet considered a form of remembrance of Allah, and is it the best form of remembrance, or is seeking forgiveness better than it?

Every remembrance (dhikr) is superior at its designated time as indicated by the Sharia. There is no evidence specifying the absolute superiority of one of these two forms of remembrance (sending blessings upon the Prophet, peace be upon him, and seeking forgiveness) over the other.

It has been narrated in a hadith that dedicating all supplication (du'a) to sending blessings upon the Prophet (peace be upon him) ensures the forgiveness of sins and relief from worries, and "prayer" (salat) here means supplication.

The Prophet (peace be upon him) used to seek Allah's forgiveness more than seventy times a day, and in another narration, a hundred times. Seeking forgiveness has been prescribed in specific parts of the prayer, such as saying "O my Lord, forgive me" between the two prostrations.

Allah has prescribed sending blessings upon the Prophet (peace be upon him) after hearing the adhan, upon his mention, and on Friday and its eve. In these instances, sending blessings upon the Prophet (peace be upon him) is superior.

Among the virtues of seeking forgiveness is what is mentioned in the master of seeking forgiveness (Sayyid al-Istighfar), and Allah's saying: {And those who seek forgiveness in the dawns} (Surah Aal-Imran, 17).

Every remembrance is مطلوب (desired/commanded), and it may be prescribed at specific times when it has a particular virtue. Absolute superiority cannot be attributed to a specific remembrance except by a definitive ruling from the Prophet (peace be upon him).