I no longer can see other devices under Network in File Explorer, a home network set as private.

Have you checked the drive on your laptop just to see, if it is working?
Especially for some SSD drives, it happens, that they just doesn't show up again anymore, if the life time is overdue.

If the drive works, what changed? Any updates? 

This sounds like maybe file & print sharing (or network discovery) was turned off on your machine.
Go to Control Panel > Network and Sharing Centre > Advanced sharing settings. Click the options Turn on network discovery and Turn on file and printer sharing.

Not sure if it's just a typo, but you've got the wrong slashes above for your manual attempt to UNC into your share device. (You've got //tp-link and they should be \\tp-link.

It would also be helpful to know if you can ping those addresses by IP. Perhaps it's a DNS issue?

@ Bembi: I just tested it on my laptop directly and it's fine. Also it's a standard HD, not SSD. Only updates would be the standard MSFT OS updates, which had 5 just last month [All in April: 5th - remove flash player/10th - Windows KB4601554 and Windows KB4589212/15th - Servicing Stack 10.0.19041.925 and Security KB5001330]. I would not be able to tell if I lost the network devices during any of these or before as it was awhile since I had looked. Thank you.

@ Andrew Porter: I had checked those, they are listed under Private (current profile) and both discovery and sharing are already ON. Also, thanks for the reminder with the \\ and not //. That might have been the issue to map the drive, as I was able to map it now. I did try to use the Browse button, and it did not show up, but I could map it anyway. The drive and sub-folders are accessible under "This PC", not the "Network" like the laptops are. This doesn't seem to let me use it as an FTP server however, which is what my intention is.

However, I'm not sure which IP addresses you are referring to, please mention.

Also, I forgot to mention above to Bembi  as well, but when I plugged the external HD into my laptop to test it, I noticed that another laptop has shown up again under Network like it had before. This is where the \\TP-Share would show up, but it didn't show up when I plugged the HD back into the wifi router. At that point is when I tried with success to map it as mentioned. 

@ Bembi: Update is positive, although I'm not entirely sure what happened exactly. I also noticed that I suddenly could not print, but could ping the printer. The printer was listed as a client to the wifi router, and rebooting the printer did not help. The intermittent appearance of my other laptop, and disappearing again made me think to take your advice to upgrade the wifi router's firmware. I removed the mapped drive, rebooted the external drive, and when I checked after while and after the wifi router's upgrades (yes, there were two upgrades), all the devices that previously showed up under Network, reappeared. The external network drive is accessible and files can be opened. So I can only assume that the wifi router's upgrade set it straight again. So, many thanks for that suggestion.