I’m not sure I understand what a library OS is; can someone here elaborate?

My understanding of this is that it is a sandbox. Providing a common interface like if it was an OS for the program to run inside, but avoiding the program to use the OS directly.

What is unclear is if it uses its own common ABI or if you use the one of the host os. I don't know why but from the project description I have a little bit of feeling that this is another vibe coded project.

A library OS is an OS that is linked directly to your program instead of being a separate program accessed through a syscall to kernel mode. About the same as a “unikernel”, but a more recent term.

Basically it lets your program run directly on a hypervisor VM, though this one will also run as a Linux/Windows/BSD process.