What exactly is a bitcoin?
There is more to a blockchain than just a linked list of hashes and a proof of work. There's more to Bitcoin than just a linked list of hashes and a proof of work. What defines Bitcoin and its blockchain are the consensus rules. These are a set of rules that determine what constitutes a valid block and a valid transaction. The blockchain is a linked list of blocks which contain transactions that conform to the consensus rules. Every block in the blockchain must also conform to these consensus rules.

One of the consensus rules is that a transaction cannot create more value in its outputs than it spends in its inputs. It can create less value, and the difference is the transaction fee. But it cannot create more value as that would lead to infinite inflation and Bitcoin would not work as a monetary system. This rule is completely independent of the linked list of hashes and completely independent of the Proof of Work.

Furthermore, there is no such an object as a Bitcoin. What people refer to as Bitcoin are simply values associated with transaction outputs. There aren't actually Bitcoins; it is solely based around the transactions and their outputs.