Ebay Standard Envelope "Delivered" - Buyer Claims Inr

Poll Question
10/16/21 - Sold a coin for $11.
10/17/91 - Shipped coin using ebay Standard Envelope.
10/21/21 - Coin marked by USPS as "delivered."
10/22/21 - Buyer sends message through ebay saying coin not received.
- Exchange of multiple messages with buyer over the next few days -
11/26/21 - Buyer sends message saying coin still not received; asks for refund.

I'm not a big-time seller, and am a bit torn over how to respond. If the buyer legitimately has not received his coin I am sympathetic. However, having come across enough shady buyers already, I'm reluctant to outright refund the buyer given its "delivered" status in tracking. The buyer himself even stated that some "strange" things have been happening at his local USPS office. I do plan on filing an insurance claim, as ebay Standard Envelope service allows, but have my doubts that it will be granted due to the tracking status.

Before I respond, I thought I'd ask - "What would you do?" or "What have you done?" if you've had a similar experience?

Thanks!

Poll Choices
 File ins claim; refund buyer only if claim is granted.
 Refund buyer; file ins claim and keep fingers crossed.
 Advise buyer to open an INR case through ebay.
 None of the above - I will explain in a reply.