Proof of work doesn’t mean the coin is harder to make. It just means that it’s harder to make a block that gets accepted & that block takes longer to produce than an ordinary block. That's why miners will typically use ASICs & not GPUs (graphics processing units).

Difficulty is an integer parameter that governs how likely it’s for a block to be accepted. This’s determined by the proof of work system & periodically adjusted.

The mining algorithm isn’t a secret because it’s specified in the Bitcoin protocol. https://video.nostr.build/f83a3d8d03eaeaa422b4b6afffaeef82adba3fa0c71957c489580a944dcb0e02.mp4