A long list and I agree with most of them.It depends on what you mean by "cosy". I think to make a fleet carrier "mine" it needs:
Oh well, I can dream!!
- A lot more customisations. More than three or four interior decors.
- The addition of collectable (or ARK based) decorations that can be scattered around the owner's only rooms. As someone else has pointed out Skyrim has this.
- Customisable pictures on the walls, taken from screen shots.
- The ability to see what is stored on your FC, even only from a distance. Ships in the hangers, piles of goods in the store and tritium containers piled up in the corner.
- The ability to change where the bar, vista genomics etc are off the main hallway.
- More rooms to discover on the carrier. For such a massive ship there is not a lot of rooms. I'd love to visit the engine room or wander the corridors exploring my ship.
- A way to interact with my crew or at least get them to acknowledge me.
- Flight controller that recognises my ship and talks to me as if I were in charge rather than some casual visitor.
- A bar keeper who is not rude to me. I can sack them, but then the next one is just as rude.
- A way to interact with equipment on the carrier. Sure there are some panels that work and the commander's chair panel was a great addition.
- A few throw rugs and cushions would be cosy.
- The ability to change the mood lighting in the bar.
- Quiz nights in the bar on a Friday evening.
- Crew that walked around the carrier and did work instead of the group of three gossipers outside Vista Genomics and the navigator taking time off to play games on his tablet.
- Christmas decorations at the right time of year, as well as other festive events from other religions, cultures and lore.
- The ability to customise my crew's uniform.
- Ground crew in the hanger.
- Being able to orientate the ship so that it gets a better view from the windows.
- Curtains at the windows.
- The ability for visiting commanders to log and leave messages for me. I have no idea whether anyone had landed on my FC.
- The ability to have adverts for the goods being fold in my market or via the bar keeper (auto generated).
For non-carrier owners I think having an apartment in a Coriolis station or planetary spaceport would be a good way to bring some coziness/homeliness to the game. A player could rent one per station, with automatic deductions for rent, in the same way as Fleet Carriers are. People can visit etc.. and a lot of the customizations outlined above would also apply to this as well.
Another way would be for there to be a captains quarters in your ship, only accessible while docked or landed for safety reasons, and some of the bigger ships having a viewing deck.
Also, being able to grab a couple of deck chairs and a table to place on planets would be great too so your CMDR can sit down and take in the views.
However, I think the true coziness that OP is desiring will only be realized once we actually do have terrestrial worlds.