Lightroom not automatically finding files stored on an NAS

I use a synology NAS and have never seen this. It always just connects. How are you connecting to the NAS? It should be through SMB filesharing not AFP. The synbology AFP implementation is not reliable, but the SMB one is and so make sure it is enabled in the setup of the synology. If both are on, your Mac should automatically choose to mount through smb as that is the standard for Macs for the last decade. The NAS vendors supply the AFP protocol for backwards compatibility but it is not needed.

Lastly, there is an old bug in Mac OS X, where it sometimes will mount network disks with a -1, -2, etc. appended to the name. Check if this is happening by looking in /Volumes on your main hard disk. If it is, unmount everything and delete all the crud empty folder copies there might be in /Volumes. Basically if it loses connection to the NAS for some reason and then later remounts it sometimes forgets to delete the mount point in the /Volumes folder and automatically creates a new one with -1 appended. When this happens, Lightroom Classic loses connection to it. You can also reboot the Mac to clean out these stale mount points.

Have you ever solved this? I have exactly the same problem. Just switched from Windows to Mac, never had any such issues. 

The green light on the left of the NAS name is off, which suggests that Lightroom does not see it. Check that Lightroom has the necessary permissions to access it.