To verify if the on-chain contract binary matches the GitHub repository, you should clone the repository locally and compile it to generate the bytecode. Once you have the bytecode, use an Explorer's bytecode viewer for a specific package to compare it with the on-chain binary. For example, you can use this link to view on-chain bytecode. By comparing the locally compiled bytecode to the one on-chain, you can verify if they match.

Make sure you compile the source code locally using the command sui move build after you clone the repository. This step will help you generate the bytecode needed for verification.