Same here.
All of my familiy's iOS/iPadOS devices are running iOS/iPadOS 14.8 and the newest update to the YouVersion Bible app is still working as it should.
iOS/iPadOS 15, to date, IMHO, is just total rubbish.
I watched YouTube videos for months on the Beta versions and have NOT been impressed with many new things in iPadOS 15.
That is why is rushed to get all if my family’s devices all caught up on the very last update of iPadOS 14, so as to avoid iPadOS 15, for the time being.
If iPadOS 15 does NOT get any better by early 2022, I may just completely skip the version of iPadOS for all of my family's devices and wait it out to see if iPadOS 16 fairs any better.
I waited many versions of iOS, previously on my own devices as iOS 11, 12 and iPadOS 13 were, also simply rubbish versions.
iOS/iPadOS 14 has turned out to really be the only decent iOS/iPadOS version, so far, to date.
Anyhoo, none of our family is having any issues with the YouVersion Bible app.
This appears to be a strictly iPadOS 15 issue that Apple needs to resolve.