System restore mysteries / shadow copies etc

(1) Your ReagentC shows partition 4 to be the Windows Recovery Environment partition. Shift+Restart will reboot to its recovery tools ("Choose an Option" screen). Normally, the computer also goes there when it has failed to boot Windows three times in a row. But going by that article I found, your computer will go to Partition 6 instead...

https://www.dell.com/support/kbdoc/en-in/000177401/restore-your-system-using-dell-supportassist-os-recovery

Restore your system using Dell SupportAssist OS Recovery

I don't see it saying it is making images or even just doing an independent backup & restore of user files. All I see is that you can do a factory reset (to the version of Windows that is on partition 5) or a fresh install of the latest Windows 10. You don't really want a factory reset after you've advanced to a greater version of Windows. It not only brings back the old version but also all the pre-installed Dell/Microsoft apps you've uninstalled along the way. And a fresh install of the latest version of Windows keeping files is what a regular reset will do anyway (without Dell's help). In either case, it will allow you to backup user files in concert with the reset & restore them afterward (but not apps). But the files will need to be accessible, i.e., whatever caused the catastrophe better not have messed with them. That's how I read it.

A Windows system image is superior because files, apps, & settings all are in the image, & apps that were deleted remain deleted when the image is restored. Also, Firewall rules are restored to that day. Only the ones you've changed since then will have to be changed again. And system images don't take terabytes. My three together occupy just 83.1 GB. A 3rd-party app could compress them even more...

That day I had to restore an image, everything was back as/of the date the image was made. But the choice is yours. And now I think your setup does possibly survive an upgrade-install because things work through BIOS & partition 6 instead of messing with the Windows recovery partition. But I really can't say for sure.

(2) That's right, Disk Management can't move a partition, & it can't expand a partition except into unallocated space immediately to the right of it. That's why a 3rd-party app is needed, but there's a bunch to choose from. It would have been nice had Dell decided to give us stuff Windows didn't already have on its own, but they didn't. If they ever do give us a partition manager, it likely will only do what Disk Management can already do.

(3) Yep, my DCOMCFG looks just like yours. Let us hope the VSS errors stay gone with Support Assist. But they almost sounded as if they could be ignored anyway. It certainly didn't keep you from getting a ton of shadow copies.

DISKPART> List Part

  Partition ###  Type             Size      Offset

  -------------  ------------  ---------  -------

  Partition 1    System         250 MB  1024 KB     <<<EFI system partition

  Partition 2    Reserved      128 MB    251 MB    <<<MSR (Microsoft Reserved)

  Partition 3    Primary        222 GB     379 MB    <<<Windows partition

  Partition 4    Recovery      990 MB    222 GB     <<<Recovery Environment partition 

  Partition 5    Recovery        13 GB     223 GB    <<<Factory reinstall partition

  Partition 6    Recovery    1309 MB    237 GB    <<<Or is this the RE partition?

Let's see "ReagentC  /Info" at an Admin Command Prompt. It will point to either partition 4 or 6 as the active Recovery Environment partition (Shift+Restart goes there)...

C:\WINDOWS\system32>ReagentC /Info

Windows Recovery Environment (Windows RE) and system reset configuration

Information:

    Windows RE status:         Enabled

    Windows RE location:    \?\GLOBALROOT\device\harddisk0*partition4*\Recovery\WindowsRE

    Boot Configuration Data (BCD) identifier: f8d976fc-df94-11ea-b1d0-74e6e2074932

    Recovery image location:

    Recovery image index:      0

    Custom image location:

    Custom image index:        0

REAGENTC.EXE: Operation Successful.

I think yours is partition 4 like mine. Then both partition 5 & 6 are expendable as soon as you begin to make system images of your own. I guess we could put a letter on partition 6 to see what's in it first...

DiskPart

Select  Disk  0

Select  Part  6

Assign  Letter=X    <<<Put letter X on partition 6

Exit

DIR  X:\  /a  /s       <<<Show contents of X:. Remove "/s" to show just the root directory.

DiskPart

Select Vol=X

Remove  Letter=X    <<<Remove the letter X

Exit

Partitions 5 & 6 can be deleted with DiskPart. Then a 3rd-party app will be required to move partition 4 fully rightward over the 14.3 GB of newly unallocated space. Finally, Disk Management can expand C:partition into that space. But we'd want you to be comfortable with Windows system images of your own (onto an external HDD) before doing so. I think Greg gave you instructions how to use Macrium Reflect. And that could indeed be worthwhile. But I am still a believer in Windows own image maker...

To backup the entire computer, make a Windows system image backup. It makes a backup of all the Windows partitions required to boot & run Windows:  EFI, MSR, Windows (C:), & Recovery. If you've got additional partition(s), they will also be offered for inclusion. (But likely that Dell factory reinstall partition won't be offered). A 2 TB external HDD is large enough to never fill with images. An 8 GB flash drive should be large enough to hold a Recovery drive (used to restore an image).

I make one after each new OS Build comes in & runs well, & I keep the last three...

I rename the computername folder which is inside the WindowsImageBackup folder (by appending the OS Build to it) in order to keep them separate & distinct. All three will be offered during the restore process.

Make it at "START, Settings, Update & Security, Backup, Go to backup & Restore (Win 7), Create a system image". Afterward, make the Repair Disc or (even better) ask Cortana for Recovery Drive to put it on USB. That can be used to do a restore. Then see the following to know how to restore one...

https://answers.microsoft.com/en-us/windows/forum/windows_10-update/how-to-restore-a-windows-10-system-image-to-an/e20992ca-5641-4f7c-bb09-3895d0732162

How to restore a Windows 10 system image to an existing or larger storage device

https://www.winhelp.us/restore-a-system-image-in-windows-7.html

Restore a System Image Backup in Windows 7, 8, 8.1 and 10

Note: That is an informative 3rd-party site, but I know nothing (good or bad) about any downloads or links that are there (or anywhere else).

If your external hard drive (or the internal one I guess) is a Seagate or Maxtor, there will be a free version of Acronis True Image at their site. Seagate calls it DiscWizard. Macrium Reflect, AOMEI Backupper & others also offer free versions of their image makers. These 3rd-party apps are quicker, make more compact images, & are more flexible in use. But the Windows version works in under 15 minutes on my small & uncomplicated system. I must add, DiscWizard's Bootable Media (to restore an image when Windows won't boot) requires a Mouse to operate. Plug one in, & it is instantly recognized.