Pantheon, Rome

I've heard that rather than completely expunge prior systems of belief, conversion into Christianity sometimes entailed integrating pagan gods as minor powers in its own mythos e.g. the casting out of Celtic deities to tir-na-nog where they eventually became the fae, or the goat-headed baphomet or horned satyr Pan becoming symbolically linked with satan

Did something similar happen with the Roman deities? Did they become lesser symbols in Christian beleif, whether good or bad? Or did they just fade away entirely?

A common claim in the occult and pagan communities is that pagan gods never stopped being worshipped- they simply were canonised as Saints by the Catholic Church. That Sainthood is a way to "worship the old gods" while also remaining monotheistic under the new state religion of Roman Catholicism established and enforced by Constantine.

I seen so many claims about many Saints having similar names or appearances to pagan gods because they are essentially the old gods. Such as Martin of Tours being Mars, Mother Mary being Diana, Jesus being Mithras, etc.

Around the world many foreign traditions blended Christianity to disguise old pagan gods with Catholicism. There is Santeria in Latin America which worships old African gods using Saint statues as disguise, Hoodo which alters African magic to be practised in a Christian framework, and plenty of Hispanic countries have local uncanonised Saints not endorsed by the Vatican such as Santa Muerte as well as customs directly from pre-Spaniard invasion. In addition many associated Catholic iconography such as the Lady of Guadalupe were attempts to use local pagan deities such as Tonantzin to make it easier for locals to accept Christianity.

So it shouldn't surprise me if there is a connection of using Saints as a proxy to worship old Roman gods. Hell in Italy there is even Stregheria and Stregoneria, a recent underground movement of witchcraft and sorcery using reconstruction of old lost Roman religion and using the Saints as a guise to worship the old gods (because Italy still has violence against pagans and accused witches). Some Stregoneria websites and Stragheria books even mentioned that the Roman paganism was never lost and as far as the Medieval ages many old Italian aristocrats and locals were already practising pre-modern versions Stregoneria and Stragheria, worshipping pagan gods and casting spells to curse others or for selfish acts such as money gains or earning someone's love.

Just a FYI tidbit, Stregoneria and Stragheria translates as witchcraft inmodern Italian with the latter being the old common word and the former being contemporary usage to refer to local witchcraft.

I am curious from the perspective of Academia and Ancient Rome studies, how accurate are these claims? Just the fact every place the Iberians conquered ended up having local syncretism of paganism and Catholicism wouldn't surprise me at all if Italians still continued worshipping the old gods as far as into the Renaissance and even Napoleonic era. I mean the Scandinavians did try to worship both Viking gods and Christian saints using the same statues in simultaneous rituals. So shouldn't something like this have happened to the Roman pagan religions and various Italic peoples and states post-Rome?

Can anyone give their input? With reliable sources (preferably books and documentaries but anything including websites will do)?