For what it's worth, I suggest you rethink your strategy.
There is no such thing as a NAS Connected USB3 drive, as NAS stands for Network Attached Storage.
I suggest that you have the direct connected storage as your data as direct connected is much quicker than NAS.
Then you can back up to the NAS using TimeMachine and then you "should" be able to browse the backup for any required file using the finder.
However, I don't trust a NAS as backup. I use one, but only as a last resort after I back up to direct attached drives.
I alternate each night between HDD and NAS.