This sort of mirrors what my experience has been during my search. In the past, reaching out via LinkedIn or otherwise would merit a response (at least); however, in the current market, I never get a reply and in some cases I see the application is rejected. I feel like sending messages is hurting more than helping.

Likewise with follow-ups. Anytime I follow-up on an interview, I never hear back or it is rejected, so I've stopped following up after interviews completely.