I think an addition to the deck would make more sense and also a lot easier to do than excavating to get that area level. An addition that os the same level as the other deck would give you avery useable addition . How big is the other deck ? I would not do any shape other tan a rectangle and size will depend on what you need for use . I happen to love decks more than patios and often design them like the an interior of a home . So a kitchen , dining room and seating space Of cours the kitchen near the actual kitchen inside works best. As for privacy a deck offers many ways to achieve that . The rocks piled up right at the wall is not a good idea and that downspout stays where it is only longer to get water a bit further away

Would advise you to hire a landscape architect or a landscaping company with a designer on staff. Either should give you some ideas that you might not have considered.

Don’t do a separate new space. It will look choppy. Just enlarge the space you already have, expanding it towards the foreground (where the picture-taker is standing).

Landscaping has limitless possibilities for privacy. A nice full ornamental-size tree or several flowering 6’ shrubs in this spot can do the trick.

love a patio on the ground!

first get the grade level, lots of fill and let it settle. Get the Drainage right.

Needs to be packed before placing pavers.

Build the patio as large as space allows. no fancy design.

At first look, I would, if budget allows, replace the garage windows with doors to the patio, even a garage door would be great to lift and create an even large patio when necessary. Plant arborvitae for privacy screen.

My point of view.

If your deck is in good condition (appears to be), adding a patio over to the right side would work to expand your outdoor area. It can be difficult to simply add on to your current deck vs. adding a patio over to the side. A deck that has been enlarged isn't just a simple (less expensive) project if you want it to look nice.

I recently had my deck removed and replaced it with a large paver patio with four different use areas (covered patio/open area/grilling area/fire pit area. My yard is NOT flat (slants to the left up next to the house) - so, two retaining walls had to be built (one steps down to a second one - this was to make the project a little less expensive (plus, I like the soft landscape that we've added).

You can make the patio various shapes - or it can be a rectangle (I would rather my patio not be the same shape as my deck). Many of the combination deck/patios that I've seen have seen also have distinct uses for the deck and for the patio.

This isn't my yard (obviously - my deck was removed) - but it shows how a retaining wall was added in order to make the area for the new patio flat.

Here is a photo of the same backyard after the patio was added. The plan for this project showed landscaping in the specific areas where dirt/mulch are currently around the patio + next to the house (you could add a landscaping bed along the back of your garage where you currently have those stones sitting up against your house).

The next photos are of back yards where patios have been added next to decks. Some are elaborate and some are simple designs:

Many have a fire pit or a pergola added:

This next one extends over to the area left of the deck + also extends across the front of the deck:

My least favorite look - a rectangular patio (without a "sit wall" or fire pit) that is roughly the same size as the deck has simply been added over to the side of the deck.

This next one has landscaping beds that were added as part of the paver patio project to make the patio appear more "connected" to the deck:

I hope some of these photos help - I saw many photos of nice looking deck/patio combinations when I did a quick search.

If your deck is in good condition (appears to be), adding a patio over to the right side would work to expand your outdoor area. It can be difficult to simply add on to your current deck vs. adding a patio over to the side. A deck that has been enlarged isn't just a simple (less expensive) project if you want it to look nice.

I recently had my deck removed and replaced it with a large paver patio with four different use areas (covered patio/open area/grilling area/fire pit area. My yard is NOT flat (slants to the left up next to the house) - so, two retaining walls had to be built (one steps down to a second one - this was to make the project a little less expensive (plus, I like the soft landscape that we've added).

You can make the patio various shapes - or it can be a rectangle (I would rather my patio not be the same shape as my deck). Many of the combination deck/patios that I've seen have seen also have distinct uses for the deck and for the patio.

This isn't my yard (obviously - my deck was removed) - but it shows how a retaining wall was added in order to make the area for the new patio flat.

Here is a photo of the same backyard after the patio was added. The plan for this project showed landscaping in the specific areas where dirt/mulch are currently around the patio + next to the house (you could add a landscaping bed along the back of your garage where you currently have those stones sitting up against your house).

The next photos are of back yards where patios have been added next to decks. Some are elaborate and some are simple designs:

Many have a fire pit or a pergola added:

This next one extends over to the area left of the deck + also extends across the front of the deck:

My least favorite look - a rectangular patio (without a "sit wall" or fire pit) that is roughly the same size as the deck has simply been added over to the side of the deck.

This next one has landscaping beds that were added as part of the paver patio project to make the patio appear more "connected" to the deck:

I hope some of these photos help - I saw many photos of nice looking deck/patio combinations when I did a quick search.

Given your slope, I'd price doing a ground-level deck. I would not do a privacy wall, but plant trees and shrubs instead. If you don't have room for trees or shrubs tall grasses or perennials will do the trick. Big bluestem and Joe Pye weed.