I had the exact same problem with a 2TB Firecuda SSHD on a PS4 Pro. It failed exhibiting the "no storage connected" message.
Because I had a couple of game saves not backed up and didn't want to reinstall my games I spent some time diagnosing the problem. In my case it was not the drive itself, but the printed circuit board (PCB). After replacing the PCB with a spare of the same model the drive spun up again, but it was not possible to recover the data at that point. This may be because I tried too much troubleshooting stuff before getting to that point, or failure of the PCB damages crucial data.
If you ever get a message of "no storage connected" with this setup – STOP immediately messing around with the drive (unless the fix is simply that the HDD slid out a little bit and needs to be pressed back into the socket). It may not help and could make the problem worse. If you are desperate, I would try replacing the PCB to see if that works (easy procedure, but hard to get the same PCB); if so using a HDD-to-USB dongle and then cloning the drive 1:1 using a PC.
I think the point of failure was when my PS4 was shutting down, but I unplugged the console right before it completely finished the shut-down procedure.
TLDR
If you use a Seagate drive of the Firecuda make, particularly the SSHD hybrid version, on a PS4 you should be aware of a high failure rate. Immediately double check that your PSN settings are set to automatically backup saves. Inform yourself about Sony's policy regarding cloud saves after Playstation PLUS expiration, and backup of your saves to a USB is recommended on occasion. Consider replacing the drive at some point with a more reliable HDD.