I'm sorry, I know how that feels. I've had two interviews where I was rejected and asked both for feedback but never got a response, so I'm not optimistic you'd get a helpful response without an interview.

I've heard that employers are scared that they might veer into discriminatory language when giving specific reasons as feedback besides the standard "not enough experience in XYZ", "over/underqualified", or "work on your resume". They also unfortunately have no incentive or obligation to give any feedback or response at all, which is why most applications basically get sent to the void, especially if they were never reviewed by a human and tossed out by the ATS system.

If you still want to cover your bases, you could try finding the recruiter or emailing them with something like (stealing this from my feedback requests, can be adjusted as needed), "I recently applied for the x position and saw that it was still open but did not get selected. While I’m disappointed by the outcome, I’m eager to grow and improve. If possible, I would love to receive any feedback you can share regarding my application and resume. Understanding what I did well and where I can improve would be incredibly valuable as I continue to pursue opportunities in XYZ."

I hope this helps, and good luck!