While the idea of Purgatory goes back to antiquity with ideas like the Fields of Asphodel in Greek Mythology and was being bounced around in Christian theological circles as early as the 7th century, Purgatory was a concept formally introduced into Roman Catholic theology in the late 11th century (or at least, Purgatory as a physical plane in between Heaven and Hell). The concept was formalized in the writings of Thomas Aquinas and then the First Council of Lyon in 1245.

The introduction of Purgatory would go on to be one of the greatest issues in the Great Schism of the Western and Eastern churches in 1054 and, five hundred years later, in the Protestant Reformation. While the Eastern Orthodox rejected purgatory on grounds of theological differences concerning punishment in the afterlife and heaven, the Reformation would push back against the concept of purgatory largely because of the practice of indulgences, "buying your way into heaven," and the concept of divine grace/"once saved always saved" rather than the practice of continually doing good works and giving money to the church in order to escape Purgatory and go straight to heaven.

Was it influenced by the way other religions treat liminality and liminal spaces?

I would say maybe, simply because the closest theological analogs to Christian (and specifically Roman Catholic) tradition, Judaism and Islam, have a very different conception of heaven and hell than Christians. In Judaism, Gehenna is considered an intermediary state where most sinners spend up to a year before being released into heaven, but it is clearly and explicitly taught as a strictly intermediary purification state with a defined time limit. Islam has Barzakh, which is on the surface similar to the Christian concept of Purgatory but is more akin to the concept of limbo (the place in between life and the afterlife) than Purgatory or Gehenna (which are intermediary states between 'heaven' and 'hell' rather than life and the afterlife).

Thank you!