How tight is your budget? Having an internal staircase would create some really nice flow between indoor/outdoor but I would consider the complexity and cost of digging up beneath the current ground floor. Have you thought about knocking through the kitchen wall adjacent to the dining room and having an entire open-plan space between the 3 areas or do you want some division?

Hey! We can be flexible on budget, knocking through the wall and not extending at all is definitely an option so we can still have open plan - our garden is just so long and not really utilised I would love more space! Just gets so tricky with the height.

Take out the wall between kitchen and dining and close off the lving room with critall style doors. You will lose quite a bit of space with an internal staircase or steps of some shape and the cost is likely to be eyewatering. As your kitchen/dining is elevated I would try and work with what you have. A wc might fit under the stairs if the pitch is steep enough.

As suggested, open up all the ground floor, include a loo if possible. Could you knock and rebuild your shed with a 'garden room' as part of it, perhaps even a second floor? Wouldn't want to block views though. Even a prefabricated building could require less foundation etc and gives a private space for interests.