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How can I completely re-install the Volume Shadow Copy Service?

I have a problem which occured out of nowhere a few months ago and which I could not yet resolve:

I cannot create Backups of my Windows 10 PC because the service “Volume Shadow Copy” throws errors. The errors occur in my backup program Ashampoo Backup Pro 15 but also if I try to use the built-in Windows 10 backup “Backup and Restore (Windows 7)”.

The 3rd party backup program yields the following error code: 0x8004230f. The whole error message roughly translates (from German) to:

Error while starting Windows component (Volume Shadow Copy Service), which is required for backing up the disk (Error VSS 0x8004230f)

The Windows Backup and Restore fails with Error Code 0x80070002 as you can see in the attached screenshot: Windows Backup and Restore Error Screenshot

I tried repairing the service using sfc /scannow and dism.

In the Windows Service console, the VSS Service is set to start type Automatic. If I manually start the Service, the errors are reported as described above.

The output of vssadmin list providers is as follows:

vssadmin 1.1 - Verwaltungsbefehlszeilenprogramm des Volumeschattenkopie-Dienstes
(C) Copyright 2001-2013 Microsoft Corp.

Anbietername: "Microsoft Software Shadow Copy provider 1.0"
   Anbietertyp: System
   Anbieterkennung: {b5946137-7b9f-4925-af80-51abd60b20d5}
   Version: 1.0.0.7

How can I fix the VSS Service and create backups again?