My 2010 MacBook Pro that has been functioning without issues before failed a High Sierra update today, and then started showing a blinking folder icon, which indicated that it was not able to locate a startup. I rebooted it with Command + R and opened the Utilities. Now, if I use Restore from Time Machine, it's unable to locate a Time Machine. If I go to Reinstall MacOS, it's unable to locate any disks for the install. Disk Utility is not showing anything except of "OS X Base System" and its parent "Apple Disk Image Media". If I run "diskutil list" in Terminal, I get a bunch of little disks that have nothing to do with the main one. Does it mean that the update failed my hard drive completely? Is there a way to restore data files from it if I get a new MacBook?
That is an older MacBook and while some Macs do last quite a while (I have a working SE/30 in my office...) it could be that the drive just failed and it was coincidental with the OS update you were applying.
If Disk Utility does not show the drive in Recovery Mode that would point to the SSD itself having (possibly) failed. Yes it could be another component or even the system board or connectors, cables, etc that connects to the SSD. But the logical first step would be to try that SSD in an external case on another Mac. If it is still not working then I would replace the SSD.
ifixit.com is a good source for instructions, tools and links to replacement drives. I have no relation or interest in the company, other than they provide an excellent resource.
Note that while it SOUNDS like a possible SSD failure, diagnosing hardware via web forum can only give you possibilities you can try. Depending on your needs it may be better to just get a new(er) Mac or have a trained Apple repair person have a look at it.
That is if you don't feel qualified to do this work yourself. After all, if you are not familiar with working on the guts of your Mac you run the risk of damaging it even more in your repair attempts.