Backup to unc path in workgroup environment
the problem are not coming from the dba tools but from your network.
You can't mount a share on a local path. That path (K) can't be seen by sql server.
The unc path works with the user that is running the sql server service, in your case the computer account; but you can't authorise the compunter account in your nas under workgroup.
The only option i can suggest you to test is to change the sql server user to a local windows user and then create a user in the nas that match it in the username and password.
Then you can try with the UNC path; but i'm not sure if it will work.