This isn't a complete answer to the question, but one big factor is the influence of Buddhist art and intellectual/religious competition with Buddhists in Central Asia. Buddhists made a lot of manuscript paintings illustrating stories from the life of the Buddha and whatnot, and a lot of elements of Buddhist art such as depiction of supernatural beings end up being borrowed in Islamic paintings of Muhammad's journey to heaven (the Mi'raj). The painters took ideas from how Buddhists painted their supernatural beings and applied them to angels Muslims believe in (the way angels are described in the Bible and Qur'an doesn't necessarily make them easy to paint--look up 'Biblically accurate angel' images if you want examples). Similarly, they applied symbols of holiness in their paintings of Muhammad. Christiane Gruber has a whole book on this topic: https://www.academia.edu/456895/_The_Timurid_Book_of_Ascension_Mirajnama_A_Study_of_Text_and_Image_in_a_Pan_Asian_Context_

Late Muslim courts, like those of the Safavids, Ottomans, and Mughals adapted the traditions established by the Timurid courts. (These paintings, or at least the ones that have survived, were commissioned by royal/princely courts, not ordinary rich people.)

As for how this started in the first place, the big turning point when Muslim manuscript painters started painting the prophet was after the Mongol conquests, and especially in the Timurid period. The Mongols supported Buddhist monks for a long time. The Timurid Empire that arose in the late 1300's was centered on Central Asia, with capitals/major cities including Herat and Samarqand, and had a lot of trade with China and interacted with Buddhism. So probably a lot of the upper class of the Mongol and Timurid empires, as well as painters and some scholars, were familiar with Buddhist iconography, and wanted to see the miracles attributed to Muhammad illustrated in a similar way.