What OS were you booting when attempting to view the files on the SSD? If macOS 10.13+ has been installed on this SSD, then it will be using the new APFS file system which older versions of macOS cannot access. You should be able to see the physical SSD even when booted to an older OS, but you won't be able to mount any APFS volumes (may not even be able to see them).
If this is a third party SSD, then you definitely need to be booted from macOS 10.13+ since older versions of macOS are unable to communicate with third party NVMe SSDs.
What are the actual symptoms of this laptop's failure?
I know both Drive Savers and OnTrack both provide free estimates and both are recommended by Apple and other OEMs. Years ago my organization used Drive Savers a few times. We were happy with the results at the time. In fact one of the drives they could not recover any data so we were not charged anything....they had told me up front it was unlikely any data could be retrieved (I suspected that was the case before even contacting them).
I hope you will begin to have frequent and regular backups in the future to help minimize the chances of data loss. With the newer Macs, there are a lot more new ways to permanently lose access to your data due to the new hardware, software, and security features.
Good luck getting your data recovered.