How does the depiction of Julius Caesar in Shakespeare's play differ from the actual events, as far as we know from Plutarch, in terms of Andrea Andreani's (1598) painting of Caesar receiving the crown from an angel?

The Greek writer Plutarch (ca. 46–120 CE) wrote biographies of many famous Romans and Greeks. His work Parallel Lives was William Shakespeare’s main source for Julius Caesar and the other Roman plays. Shakespeare almost certainly used the 1579 English translation by Thomas North, which was in turn based on Jacques Amyot’s French translation of the 1560s.
Plutarch’s views of the character of the Romans who ended up being conspirators to kill Caesar strongly influenced Shakespeare. Some of Shakespeare's text closely echoes the North translation, such as Antony's descriptions of Caesar’s generosity. According to Plutarch, when Caesar returned from his successful African campaigns, he spoke to the people about his victories and made them numerous gifts. In this oration, Caesar

greatly praised and commended this his last victory, declaring unto them that he had conquered so many countries unto the Empire of Rome, that he could furnish the commonwealth yearly with two hundred thousand bushels of wheat, and twenty hundred thousand pound weight of oil . . . [H]e very liberally rewarded his soldiers: and to curry favour with the people, he made great feasts and common sports.

The Renaissance fascination with the classical world, which extended throughout Europe, was very strong in England. The Italian artist Andrea Andreani produced a set of woodcuts in 1598 to 1599, collectively known as The Triumphs of Caesar, which were adapted from paintings with the same title made a century earlier. The paintings by Andrea Mantegna were commissioned by the a duke of Gonzaga family for their palace. Caesar on His Chariot, plate 9 of the prints, like the original painting, depicts an angel placing a laurel crown on Julius Caesar’s head as a man reaches a staff bearing another crown toward him, amidst crowded streets. The depiction of the angel, associated with the Judeo-Christian tradition, is one element linking ancient Rome to modern Italy.
Plutarch also refers to the widespread support to crown Caesar king and how the actions in favor of this also roused the opposition, who wanted Brutus at their head.

Caesar's flatterers . . . beside many other exceeding and unspeakable honours they daily devised for him, in the night time they did put Diadems upon the heads of his images, supposing thereby to allure the common people to call him king, instead of Dictator . . . Now when Cassius felt his friends, and did stir them up against Caesar, they all agreed and promised to take part with him, so Brutus were the chief of their conspiracy.

Plutarch also describes how Antony, in his funeral oration, showed the people Caesar’s bloody robe—the specific image that Shakespeare uses.

When Caesar's body was brought into the market place, Antonius making his funeral oration in praise of the dead, according to the ancient custom of Rome, and perceiving that his words moved the common people to compassion: he framed his eloquence to make their hearts yearn the more, and, taking Caesar's gown all bloody in his hand, he laid it open to the sight of them all, shewing what a number of cuts and holes it had upon it.
https://archive.org/stream/shakespearesplut02plutuoft/shakespearesplut02plutuoft_djvu.txt

https://oll.libertyfund.org/titles/plutarch-shakespeares-plutarch-vol-i-containing-the-main-sources-of-julius-caesar