Where does the door lead? Kitchen? Hallway? If possible I would change that door to a slider for more light in the house.

Due to the slope I would do a 2 level deck: the top one for seating and the lower for BBQ. I would hate the way that window is blocked.

The door leads to a hallway (see photo above). The window is in the bathroom :)

Steps to a large patio with room for seating, grilling and whatever else you want to do in the yard. A "patio" can also be a low deck. Here are my "before and after" shots of tearing off my deck.

Edited to add that the advantage of a patio is you are down looking out at your yard. A deck is fine if you have something nice to look OVER and out at. But either way, don't skimp on size for what you plan on using it for. I was limited by the tiny size of my yard. That's why a patio was nicer, more privacy and no more views of tops of neighbors heads. We did have to grill relatively close to the windows, but we were so tight that even our neighbors grilling wafted into our open windows. Luckily my neighbor who did the most grilling was a good cook who shared . . . My other neighbor created a grilling patio opposite his one beside his house. It was against the garage wall, but it was a short walk as you can see in the photo.

Yes! Plan is to add a small patio with Interlock and to have as much green space as possible! The tricky thing is that the back door is so high up! We need some kinda landing :)

What are all the benefits are you expecting to achieve by a makeover?

Apparently privacy is a driver here so I’d go for two levels. The upper for grilling and lower for seating, with a combo of fencing and plantings. A row of cedars would be immediate but I think you can do better with plantings that mature well and are a mix of color and texture.

Everyone thought I was crazy for tearing off my deck, but it was a privacy issue. In my tiny space, a deck offered zero privacy and was hot as hades and windy. I couldn't get nice potted containers to grow well and my view when sitting was of railings that looked like jail bars.

From what I saw in my tight neighborhood, you could go for a small porch look, (with a roof or awning) and then use bamboo screens on the side for more privacy and additional shade if needed. Get a small enough grill (we had a portable Weber with a stand) that you can move it up and down and away, so that you're only grilling close to the house in ratty weather. The key for the porch is some type of roof, which will shade it in summer and make it possible to grill out there in winter. The windows will be closed then anyway. You have a farther down ways to go than I did, mine was only 3 steps so no porch needed really. I often wished I had a larger stoop though.

You could also go for a deck gradually layered down to a low deck, but since concrete patio is the cheapest, go for that. That was my greatest regret, is that I let a landscape designer talk me into the pavers for my patio. She worked with a company that supplied them but the ones I chose were the least expensive and just not that great looking with the brick of the house. OK but not great and concrete would have been cheaper and easier to maintain and would have looked better.

I don't know about you, but I'm always seeing this ad on my Houzz page that shows photos of some of those gradual decks with landings. Not sure how safe they are . . .

https://www.houzz.com/magazine/what-to-know-about-adding-a-deck-stsetivw-vs~30420456