Increasingly the scholarly consensus around Constantine's conversion was that it was a genuine conversion motivated out of sincere belief. The idea that his conversion was a political or secular ploy to solidify his own power is a holdover of the late 19th and early 20th century.

Constantine had been governing to the benefit of Christians and at the expense of pagans in the empire for quite some time before his death and baptism. The famous Edict of Milan issued toleration and the return of confiscated property to the Church. Eusebius, perhaps erroneously, claims that later in life he oversaw the destruction and looting of numerous pagan temples. However, many pagan temples and pagan thinkers were able to continue to practice openly throughout and after his reign, despite his Christian bias.

In between these moments there were other steps that he took to make Christianity the religion of importance in the Empire. Most famously, he oversaw the Council of Nicaea and was an active participant in determining what constituted Church orthodoxy, even if he was never able to wholly reconcile trinitarian views against Arianism. The fact that he took such an active role in the affairs of theology again do indicate that he had sincere Christian beliefs and wanted the Church to be able to identify what was true and what was not. He was also noted to crack down on other branches of Christianity that were condemned as outside the norm, such as the Donatists of North Africa, but he was never fully able to bring about a full crack down on Arianism, and even may have harbored some Arian sentiments.

However there are some issues with the narratives that have spawned around Constantine's life, and death, in part due to the unreliable sources that we have for these events, looking at you Eusebius.

Eusebius, the chronicler (not to be confused with the Eusebius who baptized Constantine), maintains that Constantine was a young convert to Christianity (at least in spirit if not in deed), but there is little evidence of his claim.

But what about the deathbed conversion itself? He had been governing as a Christian ruler for years by this point, and his allegiance to the faith was quite clear. There is no indication whatsoever that he was refusing to undergo baptism out of some sort of reservation about his Christian beliefs. Instead, his baptism coming so late in life was not all that unusual for the time.

Sources:

Peter Brown, The Rise of Christendom

Ramsay MacMullen, Christianizing the Roman Empire 100-400

Eusebius, Ecclesiastical History and Life of Constantine