How can I repair my Windows 10 on a full-disk-encryption setup with VeraCrypt?

This might not be the most efficient solution, but at least a working solution:

1. Use your VeraCrypt Rescue Disk¹ to permanently decrypt your disk. This will take a while. After that, the VeraCrypt bootloader will still be active, but instead of providing a password, you can just press Esc and Windows will boot (as it is decrypted already) and most probably fail again.
2. As your system drive is now readable, you can boot from a Windows 10 installation medium and repair your Windows installation. In my case, most options did not help and I had to revert to a previous Windows Recovery Point. After that, I was able to boot into Windows again.
3. (Optional) Reapply all Updates. This time, they worked in my case.
4. As the VeraCrypt bootloader was not removed through the permanent disk decryption, you can do it now: Just open VeraCrypt and click on System > Permanently Decrypt System Partition/Drive. This will not decrypt anything again in this case, but it will remove the VeraCrypt bootloader.
5. After that, you can reapply full-disk-encryption.

¹ As long as you do not have to restore the VeraCrypt Boot Loader, key data (volume header) or the original system loader, you do not even have to use the original VeraCrypt Rescue Disk, that has been created for your particular disk. You can use any VeraCrypt Rescue Disk. Well, you should probably use at least a matching VeraCrypt version. This question confirmed this earlier. I can confirm it for VeraCrypt 1.24-Update7.