I have been frustrated by this broken update too. It keeps appearing in my update list, trying to install, and failing.
Some digging this evening revealed that I didn't even have a Windows Recovery Partition. The key info was from this list of known issues from an early accepted answer on one of the original threads on the subject.
It said:
"Important: If your Windows device does not have a recovery environment configured, you do not need this update (KB5034440). In this case, the error can be ignored.
To determine whether your device has a recovery environment configured, inspect the WinRE status by following these steps:
- Open a Command Prompt window (cmd) as admin.
- To check the WinRE status, run reagentc /info. If the WinRE is configured, a "Windows RE status" field will appear in the output, with value "Enabled". If WinRE is not configured, this field will have the value "Disabled"."
I wasn't happy with the suggestion that I could just ignore it so I tracked down an article about Microsoft's "Show or Hide Updates Tool" and used it to attempt to banish KB5034441. It still shows in Settings -> Windows Updates with the "Error Encountered" blurb, but I'm hoping a reboot will make Windows ignore it rather than me having to. Fingers crossed.
P.S. **** Microsoft?