I finally got a job.

Over a thousand cold applications with no human reply.

One referral (of many) resulted in one interview. I knew one person at the company (worked with one of their family members a decade ago), and had an information session with another one with prompting from my contact. Those two people were on my three-person interview panel.

I know this isn't helpful for people who are just starting out, but... cold applications were a complete dead end, at least for me. Just a data point for those still looking.