Chosen Solution

Apple Repair said the factory installed SSD (Samsung) was unrepairable and would cost $1900 to replace. I purchased a new 256gb OWC Aura SSD for $220 from ifixit.com (I live in New Zealand so shipping is a little more). I installed the new drive into the 2014 Macbook Pro Retina and it is not detected in the Recovery menu (after holding CMD + R on startup). Is not visible in the menu in Disk Utility from Recovery Menu.I made a bootable HD using an old USB2.0 drive and tried to find it using Disc Utility, is not visibleChecked the ‘Show All Devices’ in Disk Utility, volume or drive is not able to be detected, it only shows the recovery partition. Is it possible there is a problem with the logic board on the 2014 Macbook Pro? That the logic board is not talking properly with the SSD? Update (02/28/2021) Here are some board and socket images

And the new memory

And the old memory

Did you follow the IFIXIT guide MacBook Pro 13" Retina Display Mid 2014 SSD Replacement making sure you disconnected the battery first? I would inspect the SSD sockets contacts and look for a cracked SSD connector case. I’m suspecting the socket is damaged.

It is possible the motherboard has been damaged. Are you sure the SSD is pushed in all the way and that the battery was disconnected while working on it?