I had to run make on the uncompressed folder. Perhaps the build-essential package doesn't come with NASM in Ubuntu? I'll need a bit more info on the error if you want me to try and help you :)
The parent commenter seems to have figured this out, but to clarify a bit for posterity: build-essential does not come with nasm on Ubuntu (or upstream Debian, AFAICT). It has to be installed separately for the Zenbleed PoC to compile (if not already installed).
After extracting the POC and installing build-essential, I still get this:
nasm -O0 -felf64 -o zenleak.o zenleak.asm
make: nasm: No such file or directory
make: ** [Makefile:11: zenleak.o] Error 127
When you evaluate Keepassium could you look into if the application honors not contacting anything on the internet? For me this is a major point of feeling secure when using the application and iOS has no way to block apps from accessing the internet.
You can also directly verify these claims using the App Privacy Report. It's a system feature that shows which domains an app contacted over the last 7 days (and how often). And it works for all apps.
Unfortunately, there is no way to _enforce_ the offline behavior of an iOS app, but being able to monitor it is already something.