You can boot the VM from a liveCD ISO and then mount the drives to extract files (share a USB storage device to easily get them off). You could also add a second virtual disk, put an NTFS partition on it (within the VM) and copy to that if you plan to rebuild the OS drive.

If you need the offsets of the partitions you could also mount them from the disk image directly via a loopback device, but that's a bit more complicated.

When dealing with Windows either on bare metal or VMs, I've often found it useful to store my more important data on a second disk so that I can easily back it up and it will survive across a wipe+reinstall of the OS.

My least favorite thing about Windows, above all things, is that it's extremely difficult to discover what's wrong with it. People just try random things until it works in most cases.

Can you post a screenshot of the BSOD? This is really not much info to go on :)

But if you can access the command prompt, then your installation is still accessible, and so are your files. But its easier to diagnose if we know the actual error codes etc.

It may be just file corruption. Try running chdsk.exe /f C: in the command prompt. If that doesn't work, try dism.exe /online /cleanup-image /restorehealth. Keep your virtual NIC online for the second command, it may try to download updates from MS if local files are corrupt and the WinSxS backups are corrupt as well.

Been a while since I had a VM but iirc it was pretty easy to have a shared directory to the VM, which is very useful to (obviously) share files but it also means that since the files aren't actually on the VM itself they'll still be there even if you remove the VM since they're not part of the image.

How I learned my lesson to have a shared directory was this: I had been having audio issues on the VM and at one point just decided to start over with a new VM, completely forgetting that the files I had been working on for a project were part of the VM and would be gone.

But really, try booting a portable version of Windows like it's a CD or USB in the VM.

Do you have an earlier snapshot that you can roll back to? If not then this is a learning experience about how you should take a snapshot before doing any configuration changes/updates. And also maybe some automatic ones on a schedule (daily/weekly).

As far as recovering files, you could try the Windows recovery environment (or whatever they call it). Take a snapshot first, in case it makes things worse.

You could also try mounting the virtual disk to your host system. https://www.baeldung.com/linux/mount-qcow2-image

Or try booting the VM with a live boot environment of your favorite distro, similar to how you would do recovery from a dead physical machine.