Running Java applications was the original mission of OSv (https://osv.io/). Reading the website now they seem to have pivoted to running unmodified Linux applications.

The rabbit hole goes even deeper. Georgios was thinking about this with Jikes even earlier: https://gousios.org/pub/gousios-mscthesis.pdf

Does it mean it can run Java compiled to Native Image?

It doesn't necessarily mean that but yes you most definitely can run native images - another example showing that: https://github.com/nanovms/ops-examples/tree/master/java/07-... . Both of these pair very well with unikernels. Especially quarkus has excellent boot time and low mem usage.

Why not full VM with JIT? Seems much easier and more compatible with apps out there.

You can also run the full JVM and in fact I'd imagine that's how most of our JVM users actually use it today.

Because the JVM is fairly dynamic so it becomes hard to know which part to prune