I suspect that the building of the "Rescue" Recovery media (on bootable USB flash drive, as well as probably also on Boot Manager menu) failed to include all of the necessary driver files to get to the network and see the NAS device. This is no different than similar issues with failing to see external USB backup devices while in Rescue booted to either way on my own ASUS Z170 machine which has both Intel USB controller and Asmedia USB controller, with my external USB backup drive happened to be plugged into a USB port controlled by the Asmedia USB controller.
In the case of my Asmedia USB story, looking in Device Manager -> Universal Serial Bus Controllers shows that there are TWO SEPARATE DRIVERS REQUIRED:
(a) Asmedia USB Root Hub: ASMTHUB3.SYS, which is tied to ASMTHUB3.INF and ASMTHUB3.CAT
(b) Asmedia USB 3.1 eXtensible Host Controller: ASMTXHCI.SYS, which is tied to ASMTXHCI.INF and ASMTHXCI.CAT
In fact, using Macrium Reflect "Rescue Media Builder" in Other Tools, either for WinPE 10 1709 or for WinRE 1903, because of what is apparently a bug (I have already reported this in a ticket, and they have collected all of my diagnostic information and forensiic evidence, and are working on the solution) the TWO DRIVERS required (for both USB3 and XHCI) were not BOTH installed into BOOT.WIM of the Rescue media. In fact, only XHCI was installed, thus making access to the Asmedia Controller impossible, and thus making my external USB backup drive plugged into an Asmedia-controlled USB port invisible.
For me the manual workaround solution (in the short term, until Macrium fixes their Rescue Media Builder problem and grabs BOTH of the needed USB drivers) was for me to manually pre-build driver folders with proper content files for BOTH XHCI and USB3 of the required Asmedia drivers, located in C:\boot\macrium\WinREDrivers\64Bit\USB\Asmedia 3.1, before pushng the BUILD button for Rescue Media Builder in Other Tools.
And now, BOTH of the needed USB drivers ARE TRULY PRESENT IN BOOT.WIM of the Rescue media (both Boot Manager and standalone USB), and my external USB backup drive plugged into an Asmedia controller USB port IS VISIBLE for selection of the recovery images.
I am guessing exactly the same issue is the explanation for your own inability to see the external NAS device, for selection of the image files contained on it.
You didn't tell us what steps you went through to build your Rescue USB flash media. Did you check the "copy host USB files" or not? And did you manually select any other additional Ethernet device driver files to be "copy from host", or did you simply accept "compatilble driver functionality already present in WinPE" and do nothing further?
But in particular can you please provide a screenshot or two of the expansion of your C:\Boot\Macrium\WinREDrivers\64Bit\Ethernet folder to show any files and further sub-folders. Underneath that folder there are probably additional sub-folders for all the network adapter devices on your machine, so if you could expand each of them as well as provide screenshots of the file and sub-folder contents as well. Etc.
Note that the \WinREDrivers folder/file structure should also be duplcated into the additional matching C:\Boot\Macrium\WinREFiles\media\Drivers\Ethernet folder structure. You should check that as well.
It is this driver folder/file driver which then makes its way into the C:\Drivers folder in BOOT.WIM of the bootable Rescue media, to be installed when you boot to Rescue (either from Boot Manager or standalone USB flash drive) in order to provide all of the additional drivers installed into WinPE at boot time. Unless all of the proper drivers needed to support the ethernet devices are in this C:\Drivers folder in BOOT.WIM, you will not have full functionality to the network and will not be able to see your NAS device or select any of the image files stored on it.
And finally, can you provide a screenshot from Device Manager showing your "network adapters" expanded. You will probably see wireless AC, perhaps Bluetooth, and one or two ethernet adapters. If you right-click on the ethernat adapters and pursue Properties -> Driver tab -> Driver details button, you will see all of the related drivers files installed that allow full functionality while booted to your operational Win10. The same drivers need to be provided in \Drivers of BOOT.WIM in the Rescue media in order to provide the same level of full functionality while running in the Rescue environment.
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