I only have a minor in art history so I don’t know if I will be able to give an answer that meets the criteria of r/AskHistorians but I’ll give it a go.

I think to answer your question it would be helpful to both analyze Perugino’s “The Delivery of the Keys” as part of a set of frescos and to look at other depictions of Judas from the same period.

Perugino’s “Delivery of the Keys” is a fresco painted 1482 on the north wall of the Sistine Chapel. Under Pope Sixtus IV the walls of the Sistine Chapel were decorated with a series of frescos depicting the life of Moses on the left-hand side (south) and the life of Christ on the right-hand side (north). There were originally eight frescos, painted between 1481-82 by several artists, depicting the life of Christ: the Nativity (painted over by Michelangelo’s Last Judgement), the Baptism, the Temptation of Christ, the Calling of the Apostles, the Sermon on the Mount, the Delivery of the Keys, the Last Supper, and the Resurrection (original destroyed and remade c. 1572). Of these eight frescos Judas is depicted in the Sermon on the Mount, the Delivery of the Keys, and twice in the Last Supper. In the Sermon on the Mount, painted by Cosimo Rosselli, all twelve apostles are depicted with halos (both in the middle and on the right). As you have pointed out, the same is true in the Delivery of the Keys by Perugino. The next fresco is where this changes. The Last Supper by Rosselli has two depiction of Judas. In the foreground Judas is depicted on the opposite side of the table from Christ and the other apostles. Judas has a halo, but it is painted a dark color. This is in contrast with the bright golden halos of the other apostles. In the background of the fresco, in the middle panel above Christ, Judas is depicted again. This time it is as he is kissing Christ during his betrayal in the Garden of Gethsemane and here Judas is depicted with no halo. Looking at the series of frescos together it can be interpreted that the halo is used symbolically throughout the narrative of the frescos. Judas being depicted with a halo for when he is still a loyal follower of Christ, the dimmed halo for when Christ declares that one of the apostles will betray him, and no halo for the moment of Judas’s betrayal.

This series of frescos isn’t the only example of Early Renaissance art that is meant to be read as a narrative. Masaccio’s Tribute Money, painted c. 1427, is a fresco in the Brancacci Chapel that can be divided into three scenes. In the center, Christ, Peter, and the other apostles are being confronted by a tax collector. On the left Peter is taking coins from a fish’s mouth after being instructed by Christ. On the right Peter is paying the tax collector. These scenes are meant to be interpreted together as depicting a series of events in a story. It should also be noted that all twelve apostles in Masaccio’s Tribute Money are depicted with a halo. Similarly, Perugino’s Delivery of the Keys should be interpreted as just one scene in the narrative created with the other frescos beside it. Although the frescos that make up the life of Christ were painted by different artists, the series of frescos were likely planned as a whole, and each were meant to parallel the frescos depicting the life of Moses on the opposite wall.

In fact, Perugino’s depiction of Judas with a halo or even Rosselli’s depiction of Judas with a darkened halo are not particularly novel when compared to other depictions of Judas from the Proto or Early Renaissance. Besides the art mentioned above there is also Giotto’s Christ Washing the Disciples’ Feet c. 1305, Duccio’s The Last Supper c. 1308-11 (Judas has no halo but neither do the apostles seated on the same side of the table as him), Fra Angelico’s Institution of the Eucharist c. 1441-42 (darkened halo) or Communion of the Apostles c. 1451-52. It is true that many depictions of Judas from the Renaissance show him without a halo, and even Perugino has a fresco depicting Judas without a halo (Last Supper c. 1493-96), but it is also not odd for him to be depicted with a halo.

As for WHY an artist would choose to depict Judas with or without a halo in a particular work of art there is no real definitive answer that can be given unless the artist stated the intent themselves. You can look at the works of the artist or the period in which the art was made to see if there was a trend being followed but, as shown above, there were no strict rules in the depictions of Judas before or during the time Perugino painted the Delivery of the Keys.

Sources: Besides the works of art linked above I also referenced the Vatican Museums’ website,  History of Art: The Western Tradition Vol. 2 6th edition by Janson and Janson, and Goffen, R. (1986). Friar Sixtus IV and the Sistine Chapel. Renaissance Quarterly, 39(2), 218-262.doi:10.2307/2862115