You just send out a generic decline, and document it as there's a better candidate fit for the role.

I'm not sure if you guys have been in charge of hiring, but there's no real alternative. In my most recent experience, we had one open position, and after interviewing 10 candidates, 3 of them were basically identical in terms of technical qualifications. How do you choose one over the other, other than the "vibes"? Anyone suggesting otherwise is either living in a weird alternate reality, or doesn't want to accept that working is a cooperative job and interpersonal relationships are very important.

There always will be exceptions for different type of roles and specializations, but that's not what I'm talking about.