I couldn’t figure exactly your current workflow, NAS setup and goals.
If I’ve understood correctly, you have a NAS which is running a Windows OS, right? I would rather call that a remote PC then, since it would be a full fledged OS, whereas most NAS usually have an embedded Linux just as a mean to manage services and interfaces.
Did you install Git for Windows on the NAS?
Also, Windows doesn’t natively support SSH, so you’ll have to setup that too (by installing some application and setting them up, and then allowing them through the firewall).
I’m not quite sure if these are two different problems or two faces of a same one.
The first could relate to Git credentials not having been set up correctly (or at all), or the lack of a credential manager (that gets installed with Git for Windows though).
The second one seems more serious, for it looks like you’re not logged in a user on the machine (hence the thought that the previous error might be relating to Windows credential instead of Git).
This is probably due to the fact the recently GitHub enforced PAT (Private Access Tokens), so you should create your PAT and use that instead of the old password whenever you’re asked for the password (the user remains the same, but the password can be used to log into GH website, but nor for Git operations, which now require the PAT instead).
Here is where I get lost … Why did you setup Git on your NAS in the first place? There aren’t many alternatives to using your NAS except via remote desktop. Unless you’re asking how to setup an SSH terminal connecting your PC to your NAS, is that it? yes, that might be faster, a tidy bit. You should install (well, just download and unZip really) PuTTY for Windows terminal + SSH, and then do a lot of configuration work on both machines (PC and NAS).
What’s your goal with all this? Being able to store your repositories on the NAS to save space, but have Git on your main PC? Well then you can just install your own Git server on the NAS, Git on your machine, and then you’ll be working with Git on your PC, storing copies of your repositories to your NAS and pushing/pulling changes directly from GitHub (all without the remote desktop, just via HTTP or SSH). But you’ll still need to have local copies of your repositories on the PC this way, at least while working on them (editing, etc.).
Git is decentralized and distributed version control system, so you’re not stuck with having just one server to work with (or even needing a server at all).