That is FOB/FCA. But the reason that there was a commercial shipping term F ‘on board’ or ‘carrier accepted’ is because it is not the only shipping arrangement that ‘makes sense’. Other terms also ‘make sense’ to different people.
FOB seems to have a different usage in N America. Elsewhere it means that the goods change hands at the point they are shipped. Free on Board is a hangover from the days of sail when disasters were more common and shipping times were lengthy.
The point at which title changes has been much litigated over the years and I have no doubt that there are volumes of precedents. I used to be responsible for shipping goods all over the world from the UK and some were FOB and some not. The difference was usually down to the ongoing relationship between my company and the buyer. FOB required payments to a third party to verify the shipment, so that was added cost.
Over the last year, there has been an enormous increase in the volume of parcels as people in lockdown switched from High Street to online retailers. Parcels can and will go astray for all kinds of reasons (theft, incompetence, poor packaging) but it is well established here that title does not transfer until the goods are delivered.
In these difficult times, getting a signature has been a problem, so the parcel companies have taken to photoing the parcel when they leave it on the doorstep or wherever. For high-value items, they do wait for a signature and when I bought the computer on which I am currently typing, the deliverer took my picture (with permission) as I scribbled on her tablet.
I notified them and they say they are going to look into it.
As per the OP, the box said “PERISHABLE” on it and I’m assuming it was shipped as a perishable item as there was dry ice in the box (all gone by the time it got to me) and I believe that needs to be reported to a shipping company.
Others have addressed the legal concerns, but my basic real-world experience in the US has been this: If you receive goods that were damaged by the carrier (this includes damage caused by delay), you contact the sender to alert them of the problem. The sender may or may not arrange for the carrier to return the damaged goods to the sender (this depends on whether the damaged goods may still have any value to the sender), and if the sender has opted to pay for insurance on the shipment, the sender can file a claim with the carrier and expect to be reimbursed for the damaged goods. Meanwhile, the sender sends a new shipment of goods to you to make you whole.
Re: your question #1, if a shipper runs their truck into your garage door or breaks your window - regardless of whatever else they may be doing at the time - they are just as liable for the damages as any other schmuck who does the same.
Re: your question #3, if a merchant refuses to make you whole after a carrier screw-up like the one you describe, IANAL but ISTM you could call your credit card company for relief. Tell your bank “I paid for frozen crabs but received 4-day-rotten crabs, and I’ve tried to work it out with the merchant, but they’re not making me whole”. Barring that, ISTM you could take the sender to small claims court.
I haven’t seen anybody question this yet, but: Would it be accurate to say that Saint_Cad paid the seller, not FedEx, for the shipping, and the seller then contracted with FedEx?
That seems like the proper reading of the situation. The OP never talked to FedEx prior to the shipment, they never talked to him, didn’t care who he was, he’s just an address to them, there’s no possible meeting of the minds. They did however contract specifically with the shipper who the OP did have a contract with.
I am no fan of FexEx either, on top of numerous undelivered, misdelivered, and late delivered packages one of their drivers once hit my car in my own driveway.
Much has been said above about thelegal position, but unlike the occasional eBay shipper, large companies like Amazon may well have special arrangements to avoid costly disputes.
If FedEx loses your goods, the supplier may well simply ship a replacement. They will of course record such losses and they will come up at contract renewal time, but pursuing them would likely be more costly than swallowing them.
I don’t know, but I think it highly likely that large suppliers also keep track of individuals who seem to suffer a higher than normal number of lost-in-transit goods.
Legal issues aside, I recommend you give it some time for the process to go through. You contacted the seller, presumably they contacted Fedex, which is now looking into it and eventually the seller will get back to you.
BTW, is the perishable item replaceable or was it unique?

As per the OP, the box said “PERISHABLE” on it and I’m assuming it was shipped as a perishable item as there was dry ice in the box (all gone by the time it got to me) and I believe that needs to be reported to a shipping company.
That’s supposed to be reported to the shipping company, but it often isn’t (cite: my job involves a lot of shipping and receiving). It’s my personal experience that FedEx and UPS drivers are usually under a lot of time pressure, and they rarely read special shipping instructions on a package; they scan the package and go by those instructions.
And even if it were properly marked “Perishable”, it might still sit for a few days. Shipping delays happen. They may or may not be reasonable in this specific instance, but even best faith efforts can still fail.
And the “Dry Ice” notice, as I understand it, isn’t any sort of rush notice to the shipper - it’s a Hazardous Material notice (dry ice sublimates to CO2, which is a potential respiration hazard in large quantities, but more than that, it rapidly expands, and an improperly ventilated package can explode.)

BTW, is the perishable item replaceable or was it unique?
Replacable
Part of this was in my last issue with RedEx, they refused to help at all. They refused to investigate saying the driver’s GPS said he was at my location. When I followed up they said they talked to the driver and he left it in my milkbox. I told the CS rep I don’t have a milkbox, he said, “You’re a fucking liar.” Yes he used the f-word. I know a few houses in the neighborhood had milkboxes so I walked down the street and say I live at 123 Main Street, the package was at 213 Main Street (with a milkbox). When I called FedEx to complain they blew me off.
So when I called FedEx this time there was no discussion of FOB or that they will work with the seller. It was effectively, “We don’t have the contract with you so piss off.” which I interpreted as, “We again don’t want to do our job so piss off.”
All legalities aside, I can tell you how it works in real life. I’ve been shipping 100+ packages a day for the last 15 years with FedEx, UPS, and USPS. If a customer reports to us that a shipment is damaged or missing, we make them whole through a replacement or refund. We then file claims with the carrier to (hopefully) make ourselves whole. Except for tracking and actual delivery, the customer is insulated from the carrier and their policies. If the customer is not satisfied with our efforts on their behalf, they can escalate the issue to their credit card company which will take their side 99% of the time. You can argue all you want about the recipient’s legal relationship with the carrier, but in real life there is absolutely no monetary reason for either party to exercise that relationship.

If a customer reports to us that a shipment is damaged or missing, we make them whole through a replacement or refund.
Hence my question. What if the shipper said, “I did my part. I sent you the item and it’s not our fault it sat on an unrefrigerated truck for 4 days.” Where would that put me legally, especially as FedEx claims they owe no liability to me. When I asked FedEx that, they said it was my problem, not theirs. So I sat down and wrote the OP.
As a followup, FedEx said that for their resolution to my complaint they will pick up the ruined items. When I asked how that helps me being out the money since all I got from the shipper right now is, “We will investigate.” they said it doesn’t help but that’s my problem, they don’t have a contract with me.
If the shipper refused to do anything, you could talk to your credit card company and dispute the charge. It’s one of the reasons to use a credit card rather than some other payment method.

Where would that put me legally, especially as FedEx claims they owe no liability to me.
Your credit card company.
And if I used a debit card?
If it has a credit card logo on it, same thing. If it doesn’t, don’t use it for purchases that need to be shipped. Besides, most online retailers only accept debit cards associated with credit card companies.
And if you can’t get help from the credit card company, you might be able to shame the shipper into making things right, by posting, factually, about your experience on Twitter or other social media. There are multiple stories about people who got large companies to act appropriately after doing so.

I don’t think it is that simple. Are people allowed to destroy my property if I don’t have a contract with them.
It is not your property until it arrives at your door.
Buyers are responsible for getting the payment to the seller.
The seller is responsible for getting the paid for item to the buyer.
The seller shoudl refund you and file a claim and refund from the shipper.

For most (I think all, but I’m not certain) products shipped to consumers, the seller remains liable until it’s delivered and that means that in some sense they own the item until it’s delivered.
Some odd things happen with stuff shipped FOB, with freight companies, etc.