AppImages do not need to be installed. They are just downloaded, made executable, and run.
Thanks for reporting this issue.
Which library exactly?
Most AppImages assume certain system-level libraries such as glibc to come with every target system (Linux distribution).
Most AppImages do not bundle everything but only those things which cannot be reasonably expected to be already present on every mainstream Linux distribution (such as Ubuntu, Fedora, and openSUSE).
Apparently your Silverblue system is lacking some of those basic libraries that normally can be expected to ship by all Linux distributions by default.
You should be able to install the missing library using the methods provided by your Linux distribution.