I've checked our shipments and this does not seem to be Exotics, so I will comment.
When a package is marked as delivered, it definitely got to the correct post office and is, therefore, the responsibility of your local postmaster. All Priority mail is insured by the post office for at least $50, so if you contact your local postmaster or your mail carrier, they are the best possibility for finding the package, as soon as it is noted as missing.
IF you have to file a claim, THEN the sender does have to get involved. But there is a waiting period, before the post office will admit they lost it, so finding it is the best solution and can ONLY be done from your end, even if initiated on the senders' end.
IF the sender attempts to call the post office, they will read him the tracking information, same as going to the website. Except he will wait on hold, typically 30 to 60 minutes. They will then tell him he needs to wait, then file the missing package claim--I don't remember for sure, but I think it was 30 days.
I see there is now a webpage
https://www.usps.com/help/missing-mail.htm
I have never used it, but you might want to go there, since it is the weekend. BTW, here in Racine, the post office is open on Saturday, so a trip there would not be in vain.
Those are the options that I am aware of. NONE are very good. Of course, it is also possible someone stole the package from your mailbox--a federal offense, but a known trend these days. I have no idea who is then responsible for the loss, USPS or the recipient, certainly NOT the vendor.
While this all happens extremely rarely, there is the option to request signed for delivery. Adds cost to every shipment and is less convenient, but I suspect then the USPS would pay the claim to the limit of their "insurance".
Hope this helps,
Ed