There are no shadows because sun light cannot go through a vessel, it's as you were in a cave. You can rely on point and spot lights, because they have a position, but I'm not sure they produce shadows in Godot. Where do you expect the shadows to be projected?
In such a closed environnment, you could rely on ambient occlusion with SSAO for example, however it's not available yet.
You can use fog, and particles (yeah, particles! you are inside a fluid, there are always particles).
You can also apply a texture on the vessel so it won't be that "flat".
You can make the world very dark and have a point light on the player and a few objects ("glowing" viruses?), so it will apear like farther objects fade to shadows. But that depends on the mood of your game this time.