The only namespace that matters here is the filesystem/mount namespace.
There is no reason you can’t access the same shared SQLite database on a common volume between containers on Linux for instance.
That is false. Whether you mmap the same file is dependent on the specific SELinux policy - which is by design, highly configurable.
I am also surprised/skeptical that the default configuration for those OSes for a shared volume/mount point would disallow mmaping by default (which is all that is required) - since what is the attack vector they’re preventing? If you can exfiltrate via memory you could just do so via read/write.
But that only works if all given processes run on the same physical machine, and not in containers/jails/VM.
You'll either have to reduce safety and usability, or drop SQLite.