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From what I understand, each node in the Tezos network takes its own snapshots during each cycle, which I assume will differ from node to node, as baking and endorsement rights are assigned randomly. But given decentralisation, how is the "leading" snapshot selected from all these nodes without relying on a central entitity?

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From the docs:

"We admit, for the time being, that the protocol generates a random seed for each cycle. From this random seed, we can seed a CSPRNG which is used to draw baking rights for a cycle."

https://tezos.gitlab.io/tezos/whitedoc/proof_of_stake.html

CSPRNG (A cryptographically secure pseudo-random number generator) explained:

https://en.wikipedia.org/wiki/Cryptographically_secure_pseudorandom_number_generator

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