I'm slightly confused by the drawings. I thought you were keeping the deck. As there isn't a lot of room between the house and the boundary, you'll need to marry up a piece of hard landscaping between the house and the slope. How you do that is dependent on the dimensions. The bigger the deck, the more difficult it is to level the bottom, grassed area. I'd opt for a similar design to @Kathm's, where you have the seating/dining area to one side of the back of the house, with a sloping or stepped path to the lower area. I don't think there's enough length in the plot to do anything else, but it's difficult without having the correct dimensions. The area immediately below the seating area, that isn't access to the lower level, can be landscaped with shrubs trees etc depending on your preferences. That would be necessary if it's paved, and a handrail of some kind would be advisable if you have young children. If you level the grass, you'll have a fairly big height difference between it and a deck, but that can be useful as you can use the space under the deck for storage, and either screen it with solid doors, or trellis depending on the direction of wind/rain and what you want to store.
It's a place where beautiful isn't enough of a word....
I live in west central Scotland - not where that photo is...
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As there isn't a lot of room between the house and the boundary, you'll need to marry up a piece of hard landscaping between the house and the slope. How you do that is dependent on the dimensions. The bigger the deck, the more difficult it is to level the bottom, grassed area.
I'd opt for a similar design to @Kathm's, where you have the seating/dining area to one side of the back of the house, with a sloping or stepped path to the lower area. I don't think there's enough length in the plot to do anything else, but it's difficult without having the correct dimensions.
The area immediately below the seating area, that isn't access to the lower level, can be landscaped with shrubs trees etc depending on your preferences. That would be necessary if it's paved, and a handrail of some kind would be advisable if you have young children.
If you level the grass, you'll have a fairly big height difference between it and a deck, but that can be useful as you can use the space under the deck for storage, and either screen it with solid doors, or trellis depending on the direction of wind/rain and what you want to store.
I live in west central Scotland - not where that photo is...