KB5034441 fails to install with error code 0x80070643.

I've found the easiest and safest workaround for Windows RE update problem is to (1) disable Windows RE, (2) change the Windows RE partition type from "Recovery" to "Primary", (3) enable Windows RE, apply the update, then repeat the first three steps, changing the partition type back to "Recovery". You don't need to resize or delete partitions. 

WARNING: The steps below involve making changes to your hard disk's partition table. Any misstep could render your system unbootable and potentially result in data loss. This may not work for everyone. Stop if your results at any step are inconsistent with those shown below. Proceed at your own risk.

From an elevated PowerShell prompt, use reagentc to check the current Windows RE state.

PS> reagentc /info
...
Windows RE status: Enabled
Windows RE location: \\?\GLOBALROOT\device\harddisk0\partition4\Recovery\WindowsRE

The Windows RE status should show Enabled. Make note of the hard disk and partition number.

Disable Windows RE.

PS> reagentc /disable

This should move Windows RE image file Winre.wim from \Recovery\WindowsRE on the hidden partition to C:\Windows\System32\Recovery.

IMPORTANT: This doesn't appear to occur in every case. Verify that Winre.wim exists in C:\Windows\System32\Recovery. If it doesn't, reenable Windows RE with reagentc /enable and stop. This file is normally hidden. Use the -Force parameter with dir (in PowerShell) to see it.

PS> dir C:\Windows\System32\Recovery -Force

    Directory: C:\Windows\System32\Recovery

Mode       LastWriteTime      Length   Name
----       -------------      ------   ----
-a---   2/4/2024 3:37 AM        1139   ReAgent.xml
---hs-  8/6/2021 8:26 PM   440718104   Winre.wim

Use diskpart to temporarily change the type of the recovery partition. Select the disk and partition using the numbers in the Windows RE location shown above.

PS> diskpart

DISKPART> select disk 0
Disk 0 is now the selected disk.

DISKPART> select partition 4
Partition 4 is now the selected partition.

IMPORTANT: Verify that you've selected the correct partition. The selected partition is marked with an asterisk and should show as type Recovery.

DISKPART> list partition

  Partition ###  Type                 Size   Offset
  -------------  ----------------  -------  -------
  Partition 1    System             260 MB  1024 KB
  Partition 2    Reserved            16 MB   261 MB
  Partition 3    Primary            237 GB   277 MB
* Partition 4    Recovery           860 MB   237 GB

Display partition details to show the partition type. 

DISKPART> detail partition

Partition 4
Type    : de94bba4-06d1-4d40-a16a-bfd50179d6ac
Hidden  : Yes
Required: Yes
Attrib  : 0X8000000000000001
Offset in Bytes: 255158386688
  Volume ###  Ltr  Label        Fs     Type           Size  Status     Info
  ----------  ---  -----------  -----  ----------  -------  ---------  --------
* Volume 2         Windows RE   NTFS   Partition    860 MB  Healthy    Hidden

Change the partition type from Recovery to Primary (normal).

If the type is 27, this is an MBR partition. Set the type to 7.

DISKPART> set id=7 override

If the type is de94bba4-06d1-4d40-a16a-bfd50179d6ac, this is a GPT partition. Set the type to ebd0a0a2-b9e5-4433-87c0-68b6b72699c7.

DISKPART> set id=ebd0a0a2-b9e5-4433-87c0-68b6b72699c7 override

List the partitions to verify that the change was applied.

DISKPART> list partition

  Partition ###  Type                 Size  Offset
  -------------  ----------------  -------  -------
  Partition 1    System             260 MB  1024 KB
  Partition 2    Reserved            16 MB   261 MB
  Partition 3    Primary            237 GB   277 MB
* Partition 4    Primary            860 MB   237 GB

Exit diskpart.

DISKPART> exit

When you re-enable Windows RE, if a valid recovery partition isn't available, reagentc will use C:\Recovery\WindowsRE as the location for the recovery image. If a WindowsRE directory already exists in C:\Recovery, rename it.

PS> dir C:\Recovery -Force

    Directory: C:\Recovery

Mode       LastWriteTime   Length   Name
----       -------------   ------   ----
d----  12/2/2020 8:57 PM            WindowsRE
d----  3/20/2022 3:10 AM            OEM
-a---  1/12/2021 4:35 AM     1139   ReAgentOld.xml

PS> ren C:\Recovery\WindowsRE WindowsRE.old -Force

Re-enable Windows RE and confirm that the location has changed. Here, it changed from partition4 to partition3, which, in this case, is the OS partition (C:\). 

PS> reagentc /enable

PS> reagentc /info
Windows RE status: Enabled
Windows RE location: \\?\GLOBALROOT\device\harddisk0\partition3\Recovery\WindowsRE

At this point, attempt to apply the Windows Update. Regardless of success or failure, complete the steps below to reverse the changes made above.

PS> reagentc /disable
PS> diskpart

  DISKPART> select disk 0
  DISKPART> select partition 4
  DISKPART> list partition

    Partition ###  Type                 Size  Offset
    -------------  ----------------  -------  -------
    Partition 1    System             260 MB  1024 KB
    Partition 2    Reserved            16 MB   261 MB
    Partition 3    Primary            237 GB   277 MB
  * Partition 4    Primary            860 MB   237 GB

For GPT partition
  DISKPART> set id=de94bba4-06d1-4d40-a16a-bfd50179d6ac override
For MBR Partition
  DISKPART> set id=27 override

  DISKPART> list partition

    Partition ###  Type                 Size  Offset
    -------------  ----------------  -------  -------
    Partition 1    System             260 MB  1024 KB
    Partition 2    Reserved            16 MB   261 MB
    Partition 3    Primary            237 GB   277 MB
  * Partition 4    Recovery           860 MB   237 GB

  DISKPART> exit

PS> reagentc /enable
...
Windows RE status: Enabled
Windows RE location: \\?\GLOBALROOT\device\harddisk0\partition4\Recovery\WindowsRE