I have two Windows systems that had (and as far as I know, still have) the same failure as you. I tried all the proposed technical solutions (i.e., resizing the WinRE Tools disk partition and the Recover disk partition) and nothing worked to resolve the update issue on my systems. I've had an IT career and, although wouldn't call myself a Windows expert, I've fiddled with various Windows versions for years. I certainly have enough career Windows support experience (application development, starting/stopping services, editing the registry, creating CMD shell scripts, etc.) to make double and triple certain that I wasn't making a command line typo.
Even though Microsoft has removed the update from their server, if your PC has downloaded it, Windows will continually attempt to install it. Theoretically, the failed update shouldn't stop other updates nor should it interfere with other apps. However, your experience seems to suggest otherwise.
I didn't have any other issues other than the repeated failure to update. However, because the update failure irked me, I managed to remove the failing update but not-installed KB5034441 and then "hide" that update so that Windows doesn't attempt to reinstall it. I don't remember where I discovered this hack workaround (I think on a different topic thread on this Microsoft Community Forum, or possibly on another Windows troubleshooting website - but I will explain what I did). You can then decide if you want to try it. All I know is that after I applied this workaround, it stopped the download errors. But, to be clear, this workaround does NOT solve the installation problem with update KB5034441.
There is a saying, "Trust but verify." To convince yourself that the following procedure will work to hide/block future attempts to install update KB5034441, you should conduct your own web search on "How to Delete the SoftwareDistribution in Windows". If you don't trust what I've documented below, if you don't trust what you read on other websites about removing updates, or if you don't trust yourself technically to attempt this, then STOP - don't go any further; wait for Microsoft to resolve the problem.
There are two parts to this procedure to disable attempting to install KB5034441:
- Deleting all Downloaded but Not-Yet-Installed Updates
- Hiding Update KB5034441 (which configures your PC to ignore ruture attempts to install this update even if it is still on the Windows Update website
1a) To delete downloaded but uninstalled updates, you must sign-on to Windows using an Administrator user account. If you don't have access to your Windows Administrator account - STOP*, you cannot go any further, so you must wait for Microsoft to resolve the problem.*
1b) Using Windows Explorer, navigate to the Windows\SoftwareDistribution folder. On my computer, that folder is C:\Windows\SoftwareDistribution (which you must do using Windows Administrator credentials). In that folder, you should see at least two other subfolders - maybe more. The two you should see are "DataStore" and "Download". If you don't see "DataStore", then you are not in the correct folder. Type Control-A on your keyboard. That should select everything in the SoftwareDistribution folder, both files and subfolders. With everything selected (highlighted), press the Delete X button on the Windows Explorer app. You may get a prompt that says you must have Administrator credentials; if you get that, check the checkbox "Do this for all current items" and click on the OK button. You might then receive a "Folder in Use" error when it tries to delete "DataStore". Check the checkbox "Do this for all current items" and then press the Skip button. If you don't check that last box, you will also receive a "File in Use" error for the ReportingEvents.log file - so press Skip again.
1c) That's it for removing the downloaded but not-yet-installed updates. I'm not 100% certain about this next comment, but I think the reference to Update KB5034441 is still in the DataStore. Because of that (or, somehow, that the PC's "memory" of KB5034441 still lingers), you must still proceed with the next step to "hide" that update (so that your PC will not attempt to install KB5034441 unless you "unhide" it in the future).
2a) On this Community Forum thread, look on page 6 of this community thread and find Sumit D's January 11 reply to Alexis Haas's post of the same date. The very last thing that Sumit suggests (without recommendation) is how to download the "wushowhide.diagcab" tool at this link https://download.microsoft.com/download/f/2/2/f22d5fdb-59cd-4275-8c95-1be17bf70b21/wushowhide.diagcab. Clicking on the link will automatically download the tool to your Downloads folder.
2b) While still signed on as Administrator, use Windows Explorer to navigate to your Downloads folder. Then double-click the wushowhide.diagcab file; doing that that will launch the tool.
2c) A new window will pop up with the title bar showing "Show or hide updates." Click on the "Next" button. It will start examining your PC.
2d) When it stops its examination, you will see two options. Select the first one: "Hide Updates".
2e) Make sure that you select/check the update KB5034441 and any other updates you wish to hide. Then click on the "Next" button.
2f) You're done with this step. Close the tool window if it hasn't automatically closed.
- LAST, REBOOT.
That should eliminate repeated update errors. Good luck!