What Is the Primary Role of SHA-256 in Bitcoin’s Proof-of-Work?

The primary role is to find a hash value for a new block header that is below a specific target, which is the "difficulty" of the network. This process, known as mining, requires significant computational effort, proving the work was done.

It secures the network by making transaction history immutable and prevents double-spending. The hash links the current block to the previous one, forming the chain.