Time to re-create recovery partition (again)
This works from within the system, with bitlocker enabled, usually without a reboot. Unless the partition scheme so f-up that you need a 3rd party tool to help...
Rebuild the Recovery partition is a "simple" process. Skip the # lines in diskpart please :D. They don't hurt, but they will cause diskpart to show the help screen more often than needed.
Step 0: Start diskpart.exe with admin rights.
Step 1: Nuke recovery partiton. (repeat if you have more than one recovery partition)
lis dis
# select system disk
lis par
# Select the "recovery" or "Wiederherstellun"
sel par X
del par override
Step 2: Shrink to have space if needed, either with diskmgmt.msc or diskpart. If your Windows has the "bugfix" from 2017 and created the recovery partition BEFORE the system partition you have to shrink by 850 MB.
list volume
# Select C: volume
select volume X
# Shrink by 250 MB
shrink desired=250
Step 3: Recreate Recovery partition. If you Windows has the "bugfix" from 2017 and created the recovery partition BEFORE the system partition you MAY have to create two partition in order to have the recovery partition at the end of the drive. Check with lis par.
lis dis
# select the system disk
sel dis X
create par pri
# Check where that partition was created. If it was before the system disk and is too small, do a second create par pri
lis par
# If everthing is fine, go on.
format fs=NTFS quick label=Recovery
# Id for Recovery partition
set id=DE94BBA4-06D1-4D40-A16A-BFD50179D6AC
gpt attributes=0x8000000000000001
You can exist diskpar.exe now. Either by entering "exit" or closing the window.
Step 4: Copy WinRE.wim and the uninitialized ReAgent.xml files from the installation Media to C:\Windows\System32\Recovery IF MISSING. Mount or open the Installation ISO, I recommend 7-zip for this. Use the right build version for your OS. Check with winver.exe. Open Sources\install.esd or Sources\install.wim, select the biggest folder of those "1 2 3 4" etc listed there. Copy the Windows\system32\Recovery contents to your normal C:\Windows\System32\Recovery. Rename the possibly existing .xml file, if you want to keep it. From Admin command, run reagentc.exe /enable. This will move WinRe.wim to the Recovery partition and set the GUID and location in ReAgent.xml
NOW retry KB5034439, and it should install fine.
That's it. "So simple" to fix the bad planning ahead which was done in 2007, when Vista came out and supported UEFI. The bad planning was to create "only as big as needed now", aka a too small, recovery partition instead of using 1 GB right from the start for this. That bad default is still there, including the latest Windows 11 Canary Insider.