Can I leave my base to look for spadonium?
Certainly. You can use the teleporter inside of the space stations in each star system to teleport back to your base. Your ship will also teleport.
The teleporters can be found in the right door of the space station (after your ship lands and rotates).
Note thay previously you needed an Atlas Pass V1 to enter this door. This is no longer needed, as the doors are no longer locked.