It sounds like you might just need to use the keycard reader for the pod bay, you should already have the security keycard. There currently isn't any way to tell what items you have so it can be hard to figure out.
That's fair! Maybe it's unsettling that they're more realistic when the overall vibe of everything else is more stylized/cartoony.
I did reference some actual orca eyeballs for the design, which also have a bit of an uncanny valley humanlike quality to them. So, in that way I would say this is an intentional effect :)