All photos on my NAS are now missing but can't be re-added because duplicates?

I was having a very similar problem to OP and found a different fix.

Using a Synology 1511+, I have a mapped network drive (P:/ which corresponds to the //NAS/photos/ shared folder). When I first installed Lightroom Classic CC, it had no problem accessing the photos there. I was importing and creating catalogs, editing etc. for a couple of days.

I came back to it a week or two later after an update and suddenly all the photos were listed as missing. As I hadn't done a ton of work and haven't done a full import of my collection yet, I ended up deleting the catalog, thinking I could just reimport and start again.

Now, when I go to import, LR sees the folder structure just fine on the left side of the dialog, but keeps saying "No photos found" on every folder I select under P:/. When I select a folder on my local drive (C:) it sees photos no problem.

I tried x022098's solution which applied to me as my local computer (Windows 10) workgroup was not matching what my NAS workgroup was set to. However, fixing that did not fix the problem. LR still says "no photos found" on every subfolder of the shared network drive.

I verified permissions. Then I realized something that had changed in the in between time... I switched to using a Microsoft account instead of a local account in my Windows OS. I had previously setup a windows credential for my NAS to continue using the correct user when accessing the shared drives. Looking into this again led me to this thread on Synology forums:
Windows 10 and Microsoft-Account - Synology Forum

I followed the suggestion to up the Maximum SMB protocol to SMB3 on my NAS (it was previously set at SMB2) and voila! Now Lightroom works with the network drive folders again... albeit fairly sluggishly (especially when initially browsing into deeper subfolders in the P:/ drive, just getting the list of subfolder names back takes a loooong time each time you click a little expand arrow).

The problem isn't finding the volume.  Lightroom seems to not see the images in it.  I tried adding the volume as you suggested but the results were the same.  It finds nothing there.  If I point to a local drive, it finds the same files (copied from that network drive). 

"Lightroom has encountered problems reading this photo. You will not be able to make adjustments to the photo".

This is not the same as your title, which implies the photos are missing. This message indicates that the photo cannot be used.

This can happen because somehow the files themselves have become corrupted. It can happen because the files are fine, but the transmission across your network is somehow corrupting the files. (And a third possible cause, several people have reported this with Lightroom Classic CC, so I don't know if there's a bug in the software causing this or not, but since you didn't tell us what version of Lightroom you are using, who knows ...)

In some cases, I get a message the Lightroom cannot locate the image.  I point it to the proper directory (the one it is already looking at incidentally) and then I get this message: The file <filename> is associated with another photo in the catalog.

Because just becuase there is a duplicate, you have to do the proper steps to locate the photo. If you are getting the message that the file is associated with another photo, it is usually because the photo has been imported into LR, and you have to find it in the Library module (click on All Photographs, sort everything by file name, and you shold be able to locate it this way).