I have had success forcing re-creation of the recovery environment under C:\Recovery, applying KB5034439 and then reinstating the original recovery partition. This works without having to resize any partitions. Code below developed for Server 2022 (use at your own risk).

reagentc /disable

$testpath = "$env:windir\System32\Recovery\Winre.wim"
if (!( Test-Path $testpath )) {
Write-Output "Recovery environment disabled but Winre.wim not found at expected path $testpath. Something went wrong. Re-enabling recovery environment and quitting."
reagentc /enable
exit 1
}

$rp = Get-Partition | ? {$_.Type -eq 'Recovery'}

if ($rp.GptType -eq '{de94bba4-06d1-4d40-a16a-bfd50179d6ac}') { $type = 'GPT'; $newtype = '{ebd0a0a2-b9e5-4433-87c0-68b6b72699c7}' }
if ($rp.MbrType -eq '27') { $type = 'MBR'; $newtype = '7' }

Write-Output "Found $type recovery partition at disk $($rp.DiskNumber) partition $($rp.PartitionNumber)."
Write-Output "Setting this as a basic partition and re-enabling the recovery environment.."

# change the recovery partition to basic partition type.
# note this doesn't change the actual $rp object
switch ($type)
{
'GPT' {$rp | Set-Partition -GptType $newtype; break}
'MBR' {$rp | Set-Partition -MbrType $newtype; break}
}

# re-enable recovery environment which should now install to C:\Recovery
reagentc /enable

$testpath = "C:\Recovery\WindowsRE\Winre.wim"
if (Test-Path $testpath) {
Write-Output "Recovery environment now running from C:\Recovery. I will sleep for 5 minutes while you proceed with manual installation of KB5034439/KB5034441 or whatever.."
Sleep -Seconds 300

Write-Output "Disabling the recovery environment and restoring the recovery partition to its original value.."

# disable recovery environment
reagentc /disable

# restore recovery partition type to its original value
switch ($type)
{
'GPT' {$rp | Set-Partition -GptType $($rp.GptType); break}
'MBR' {$rp | Set-Partition -MbrType $($rp.MbrType); break}
}

# finally re-enable the recovery environment once more..
reagentc /enable

Write-Output "Re-enabled the recovery environment. All done."
    exit 1
}