The teleporter should be access-free

[Embolism]

The teleporter at the space diner is freely accessible to anyone with a pod or mining access, isn't it?

I think you're getting confused with the space prison, and no you need sec access and you have to build it.

The Space Prison no longer exists and there is a teleporter in the Space Diner. Anyone can use that.

So no the station teleporter doesn't need to be free access.