(1) Yep, BCDBoot, in regenerating the boot files, these days will break contact with the internal recovery environment that is on the Recovery partition. It gives you a new BCD (Boot Configuration Data) store & other boot files that should have worked, but without good entries to use the Recovery partition. It can be repaired, if we can get you booted back to Windows. In the meantime, right, use the external one.
(2) DISM & SFC did work for me in the external recovery environment. I didn't have to use /ScratchDir. The output is below. I don't know why you have permissions issues.
(3) Let's see whether you can boot to Safe Mode with Networking. Get to the Command Prompt, & enter...
BCDEdit /Set {Default} SafeBoot Network <<<Those are pointy brackets
Close the Command Prompt, then Click "Continue" to hopefully boot to Windows Safe Mode. If you get there, see whether SFC & DISM will run at an Admin Command Prompt...
DISM /Online /Cleanup-Image /RestoreHealth
SFC /Scannow
To get back to Normal Mode, enter...
BCDEdit /DeleteValue {Current} SafeBoot
Then reboot. I hope that does it. Good luck.
Here was my output in the recovery environment...
Microsoft Windows [Version 10.0.19041.1288]
(c) Microsoft Corporation. All rights reserved.
X:\Sources>DiskPart
Microsoft DiskPart version 10.0.19041.964
Copyright (C) Microsoft Corporation.
On computer: MININT-OP0NSSM
DISKPART> List Vol
Volume ### Ltr Label Fs Type Size Status Info
Volume 0 E DVD-ROM 0 B No Media
Volume 1 C PCR Hard NTFS Partition 930 GB Healthy
Volume 2 ESP FAT32 Partition 99 MB Healthy Hidden
Volume 3 WinRE 21H2 NTFS Partition 847 MB Healthy Hidden
Volume 4 D ESDUSB-21H2 FAT32 Removable 14 GB Healthy
DISKPART> Exit
Leaving DiskPart...
X:\Sources>:1 DISM /Image:C:\ /Cleanup-Image /RestoreHealth /Source:ESD:D:\Sources\Install.esd
Deployment Image Servicing and Management tool
Version: 10.0.19041.746
Image Version: 10.0.19044.1826
The scratch directory size might be insufficient to perform this operation. This can cause unexpected behavior.
Use the /ScratchDir option to point to a folder with sufficient scratch space. The recommended size is at least 1024 MB.
[==========================100.0%==========================] The restore operation completed successfully.
The operation completed successfully.
X:\Sources>SFC /Scannow /Offbootdir=c:\ /Offwindir=C:\Windows
Beginning system scan. This process will take some time.
Windows Resource Protection found corrupt files and successfully repaired them.
For online repairs, details are included in the CBS log file located at
windir\Logs\CBS\CBS.log. For example C:\Windows\Logs\CBS\CBS.log. For offline
repairs, details are included in the log file provided by the /OFFLOGFILE flag.
X:\Sources>