There have been quite a few threads about SMB differences between S1 and S2 products, but let me summarize. 
 

S1 does not have the space available in its kernel to run anything other than SMB v1. So, if you’re running S1, your NAS needs to be able to be read using the old ( and deprecated) version of SMB. 
 

S2 runs on newer hardware that has more memory available, Sonos was able to update the version of SMB in that software release. S2 will operate either SMB v2 or v3, your NAS should be supporting either of those protocols. 
 

Some NAS updates have ‘helpfully’ turned off SMB v1, and you need to go back in to the operating system for the NAS and turn it back on specifically. I’ve experienced this issue with Western Digital, I’d think there is a similar possibility with QNAP. 

Just to clarify, I’m running S2 now and my QNAP is set to SMP S2/S3 but not able to add my library.  Are you saying I should re-enable S1 and, if so, why if both are set to S2/S3?

Hopefully, I did not say that. You said you’re running S2, and your NAS is running SMB 2 or 3 as suggested, then I’d suggest contacting either Sonos Support directly, or even QNAP to find out what is getting in the way of the connection. 

Ok gotcha, I have a copy of my library on an external hard drive connected to a computer that is on 24/7 also so I was able to get it indexed so at least I’m up and running. I’d still like to use the NAS though so when I get some free time I will give them a call. My limited experience has been less than inspiring with Sonos customer service though so may still try to figure out what’s up with it on my own. 

Just so you’re aware, Sonos accesses data on local drives in a different manner than it does on an NAS (SMB required). I suspect there’s something blocking the ability of the speakers (running a Linux kernel) in accessing the data on your QNAP. Not sure what that is, could be any of an assortment of blockers, which is why I’m suggesting you contact Sonos with hard data, or QNAP. Sonos would be able to see the denial error in the data, I’d think, as long as you run it within 10 minutes of a failure/error. 

Is the NAS folder set to public or under a public directory?

As said, support are the only folks that can see the real error message so all folks here can recommend are possibilities.

I am getting the same error with a Brennan B3 device set up as a NAS.  Contact Sonos support?

You could look through these first but only Sonos has access to the internal error messages.

https://support.sonos.com/en-us/search?q=nas

Just spitballing here, but have you tried passing the UNC path to the NAS using the NETBIOS (technically NETBIOS over TCP/IP, a/k/a NBT) name instead of the IPv4 address? If you don’t know what it is off the top of your head, just fire up a Command Prompt/Windows Terminal window and use the NBTSTAT command as described here. I couldn’t venture to guess what the issue might be from the little information we have right now, but I’ve had my Sonos S2 system playing music off of my own QNAP for a couple years now with not so much as a hiccup and I define the UNC using the NBT name, not the IP. Perhaps it has to do with the fact that NETBIOS resolution shifts the SMB traffic to port 139 instead of the modern default of 445? *shrug*

The definitive approach to solving your issue is going to be with the use of a network traffic capture and analysis program like Wireshark. On the upshot, at least it’s free and has gotten easier to use in the last few years. Just get it installed and running and set a pair of filters: one for IP addresses matching either the NAS or the speaker and the other for IPv4 port matching either 139 or 445 and then “Start Capture.” Switch back to the Sonos Controller window and try to add the UNC path to the Local Library folders a couple of times, then back to Wireshark and “Stop Capture.”

You’ll have a nice list of all the packets that just passed between the two complete with their contents so you can just read the status messages they exchange and see exactly where the process breaks down. Or if you only see packets from just the speaker, then you know the issue is either the NAS is not answering on those ports and needs to be reconfigured or your network gateway is dropping the traffic before it can even get to the NAS. I’m not saying that it won’t involve a little work and probably a fair amount of “Google-Fu,” just that by the time it’s over at least you’ll know right where the problem is and more than likely have fixed it.

Best of luck to you. I know how maddening this stuff can be.