Very little, at least on the level of the central doctrines. There are certainly many examples of traditions being repurposed and Christianized: the origins of Christmas is hotly debated, with some evidence (but by no means conclusively!) suggesting the date may have been set to line up with the winter solstice and perhaps compete with or co-opt other traditions. The devotion to saints in the Middle Ages could also be interpreted as replacements of local deities, though more in popular piety than official doctrine.

But claims that the Trinity or the events of the life of Jesus were somehow ripped off from Egyptian mythology or whatever else are, frankly, rubbish. A lot of that connection with Egypt comes from the work of a man named Gerald Massey in the 19th century and was popularized by Zeitgeist more recently - and it's largely fantasy. N. T. Wright makes an excellent and thorough case in his Christian Origins series that the idea of the resurrection of Christ is very much a novel one, not meaningfully connected to anything that came before.

So my answer in a nutshell would be, in popular piety and folk traditions, there's a lot of repacked or "baptized" pagan stuff; but in official doctrine, that's not the case at all.

Hello. I cannot answer this question but a question regarding the concept of saints is discussed here.

Also, as a followup question, what is the current status of the development of Christian ideas like the "saints are just a Christian repackage of deities," in today's academia. Is it well accepted in academia and r/askhistorians is in the minority or is it the other way around? Or is it that the history department rejects that idea and other departments still hold on to it?