Since each Bitcoin node only connects to a limited number of other peers, it's hard to measure the exact count of all Bitcoin nodes. There are a few projects that actively crawl the network to provide statistics, though. Easier to measure are nodes that accept inbound connections. They're also often referred to as "public nodes", "listening nodes", or "reachable nodes". According to bitnodes.io there are currently about 14 160 reachable nodes of which 13 600 have a full copy of the blockchain. The DSN Research Group reports 8 700, coin.dance measures 14 860 reachable nodes.
Beyond that a lot of businesses and individual users run their own nodes to perform validation of the blockchain. Statistics for such "private nodes" are more elusive, but Luke-jr estimates that there are around 34 600 nodes with the full chain—since the same statistics only estimate 4 370 listening nodes out of those, likely there are a lot more non-listening nodes Luke-jr's node doesn't hear about.
So, we can conclude that there are in the ballpark of 35k to 100k complete copies of the full Bitcoin blockchain. As every new node that joins the network has to process the full blockchain, this data is frequently redistributed. Given that there are a lot of businesses and individuals with vested interests in being able to provide the full blockchain, there seems little to no chance that the whole chain goes extinct. We know that there are copies of the blockchain in numerous different countries, and at least one on a satellite in space. I'm pretty sure that there are also some in Faraday cages, in vaults, and on airgapped systems. Even if some sort of catastrophic event took out almost all copies of the blockchain, the network could repopulate from a single complete copy. I think we're good.