Your Disk Management (DM) matches DiskPart in what it says is the nutty order of those partitions, (keeping in mind that DM never shows the MSR). So your Linux partition is partition 5 but it precedes partition 4 on the disk. That's scary enough. But, on top of that, DM says it is Disk 0 that holds those partitions where DiskPart says it is Disk 1. (You've got a Disk 1, but it doesn't have those partitions.)
DISKPART> sel disk 1 <<<Disk 1 was selected
Datenträger 1 ist jetzt der gewählte Datenträger.
DISKPART> list par <<<And here are the wacky partitions
Partition ### Typ Größe Offset
------------- ---------------- ------- -------
Partition 1 System 100 MB 1024 KB <<<EFI
Partition 2 Reserviert 16 MB 101 MB <<<MSR
Partition 3 Primär 203 GB 117 MB <<<Windows
Partition 5 Unbekannt 19 GB 203 GB <<<Not a known partition type - Linux
* Partition 4 Wiederherstellun 521 MB 223 GB <<<Recovery
Your BCDEdit & ReagentC look OK to me. The latter agrees with DM that the partitions are on Disk 0.
Did you say you tried to delete that Linux partition. Are you still willing to do so? It's in a nice enough spot that you will be able to extend C:partition into the 19 GB of freed space. DM can do that, after you delete the partition in DiskPart. Let's see this...
DiskPart
List Vol
List Disk
Select Disk 0
List Part
Select Disk 1
List Part
Select Disk 2
List Part
Exit
It's worth one more look before we do the delete.
BIOS probably would continue to work as is, but I'd want to remove the Linux entries. Also, I must admit, I can't quite tell whether it is booting to the Windows Boot Manager or directly to the disk (whatever that is)...
I don't think mine names the disk, but just says "Windows Boot Manager". If you can get it like that, it would be best. Yours looks like a list of disks, but really they are all the same disk which likely is Disk 0. I suppose the bottom 2 go to the same Linux partition 5. The top one goes to EFI partition 1, I guess.
Let's see the whole BCD: BCDEdit /Enum All