(1) HarddiskVolume1 is the 1st partition on Disk 0. It begins counting with the partitions on Disk 0 & progresses to the other disks, if any.
(2) HarddiskVolume3 is your 3rd partition on
Disk 0. It is your Windows partition. ReagentC shows it also contains your Recovery Environment (to which Shift+Restart will boot). Normally, that would be in a partition of its own, but I suppose Bootcamp wanted it this way. It could happen
this way in other circumstances as well. When I briefly dual-booted, the second Windows installation was like that. (The first kept its existing Recovery partition to itself.) It updated OK, so I doubt that's the problem.
(3) I suppose that unknown partition 2 of 91 GB is your wife's "MBA" which I suppose is Apple's OS. I don't know why it intercedes between EFI & Windows. Doesn't seem right, but I know nothing about it.
(4) You are right, the issue for you is not that EFI has a wrong type ID. That's the right one. Normally, the size of EFI these days is 100 MB, but 300 MB is OK too. Maybe Bootcamp wants it that way, I don't know. But I would give it GPT attributes that
looks like helzayat's & mine this way...
https://docs.microsoft.com/en-us/windows-server/administration/windows-commands/gpt
GPT
At an Administrator Command Prompt, enter these commands...
DiskPart
Select Disk 0
Select Part 1
GPT Attributes **=**0x8000000000000000
Detail Part
Exit
But it just doesn't sound like that is a solution to the update failure. Also, I don't know whether Bootcamp wants it that way.
(5) What I like least is that you are missing the MSR (Microsoft Reserved) partition. These days it is 16 MB & located just before the Windows partition, if Windows creates it during a clean install. It used to be 128 MB. All GPT disks are supposed to have
one...
DISKPART> Select Disk 0
Disk 0 is now the selected disk.
DISKPART> List Part
Partition ### Type Size Offset
------------- ------------- ------- -------
Partition 1 System 99 MB 32 KB
Partition 2 Reserved 16 MB 100 MB <<< MSR partition
Partition 3 Primary 930 GB 116 MB
Partition 4 Recovery 790 MB 930 GB
DISKPART> Select Part 2
Partition 2 is now the selected partition.
DISKPART> Detail Part
Partition 2
Type : e3c9e316-0b5c-4db8-817d-f92df00215ae
Hidden : Yes
Required: No
Attrib : 0X8000000000000000
Offset in Bytes: 104889856
There is no volume associated with this partition.
DISKPART>
(6) Do you have other disks & does any have another EFI partition on it? That could confuse Windows during a reboot to complete the installation of an update.