No sorry, the phone logs do not seem to have more detail, they start just after this incident (I believe I restarted the app to try and debug this). And no I do not store my Vault in iCloud, it is local.
As best I remember: I had sync to pdf enabled on my desktop already before installing the phone app. Upon installing the phone app I signed in and enabled sync, then browsed around. Then I saw I was still waiting for some files, and remembered I had to enable all file types, so I opened the sync add-on settings and enabled all the optional file types, at which point my images and pdfs and whatnot showed up. I cannot say at which point this specific pdf was deleted.