Open your inventory and you can push a button to switch to the ship. It works anywhere on the ship. If you aren’t sure which button opens the ship’s cargo (I have it set to Q but I think that’s a custom keybinding) it will say at the bottom of the inventory screen which button to press to open the cargo hold.
You can also access the ship’s cargo when interacting with merchants and sell things directly from the ship.
These are the small moments that define a relationship. Your gf wants to have a quiet morning browsing her phone and you want to have a conversation. It is up to you if that is ok or not - your relationship should make you happy. You can decide that you are happy to give her a quiet morning, or you can decide that it makes you feel too weird and find a new relationship with someone that you are more compatible with. Every relationship involves compromise but only you can decide what compromise is right for you.