I use BIBM and when I installed Windows 10, I used filler partitions in the MBR to force Windows to place the recovery info in the Windows partition ("C:" drive). I prefer to have everything contained in one partition, as I think that this simplifies backup and restore when there are multiple bootable partitions present.
I have just looked at my Windows Update History, and KB5034441 seems to have installed without problem. My Windows partition in 126 GB, with 47 GB free. I don't use BitLocker.
Although having the recovery info in the Windows partition may be contributing to your problem, it looks as though there is some other problem with your system that is causing KB5034441 to fail to install.
-- from CyberSimian in the UK