Putting a raised bed next to a fence creates a couple of problems... an unmaintainable gap next to the fence, or decay if it abuts the fence ... or a worthless, skinny strip of grass to maintain if there's a wide enough gap. Is your soil horrible? Do you really need to have raised beds? If not, create beds flush with the ground and you can put them next to the fence with no problem. Then, use the stone inlaid into the ground so that it is flush with the surface and acts as a mowing strip. It will look better than being raised. Instead of separate raised beds, you could have a bordered strip bed as long as you want it.

Do you mean grow vegetables in raised beds? Or simply decorative raised beds?

If you are looking for an ornamental set of raised veggie beds, look at images of parterres and adjust for making it a kitchen garden. The geometry of the garden helps make it ornamental. For instance, look at this parterre which is planted to flowers. (Sorry for the link but it won’t post with the Houzz photo button.)

https://www.houzz.com/photos/summer-2012-traditional-landscape-milwaukee-phvw-vp~2864219

A similar design using low raised beds and your limestone for paved paths would be lovely. You can loosen the native soil, add a layer of compost, and then make a less deep raised bed. The veggies will send roots into the native soil as well as it will improve over time due to the compost. You don’t need to have such high bed sides.

This one is planted to herbs but has shallower beds and paving between.
https://www.houzz.com/photos/traditional-kitchen-garden-traditional-landscape-phvw-vp~19122726

This one has beds closer to the height I am envisioning or a bit taller, but I would keep them below a foot in height.

https://www.houzz.com/photos/forest-garden-asian-landscape-san-francisco-phvw-vp~96170109

One of my neighbors had for many years a pie-shaped parterre, round with wedges.

You would most likely want to remove your current bed to create your parterre so that it has a logical symmetry within the yard. Perennial veggies like your cardoon or artichoke or herbs can help with the symmetry. Grow an indeterminate tomato or beans or peas up obelisk trellises in the same spot in each bed. If the beds and certain key plants or structures are symmetrical, all the plants don’t have to be. Adding a center feature such as a bird bath or obelisk will add to the ornamental feel.

It seems like your placement of the current bed to allow just enough room to mow and the dogs to run makes sense.

Lots of options here! Looks like you have limestone. The stones can be utilized as edging for your planting beds, a patio, and retaining walls. Take a look at the limestone outcropping photos here: https://www.vanzelst.com/gallery/elevated-bluestone-patio-ringed-limestone-outcropping/.

Some of this information from your previous posts would be helpful in giving you a good answer.

I would like to add an edible garden but don't know a good design. I'd love paths also. The entire yard gets full sun 8+ hours a day. I’m in Zone 8b Austin Texas. Fruit trees are small, no shade. Looking to add to current beds and not have to move these. I have a part of my yard that slopes down to an easement and seems to collect water. Other than this area it's dry. The current raised bed is on the east side of the yard the fruit trees are on the south side of the yard. Patio is 12’ x 15.5’ and need design ideas for an outdoor dining space

I also think the photos in [this older post[(https://www.houzz.com/discussions/backyard-help-with-raised-beds-dsvw-vd~5626587) and [this post about the outdoor patio[(https://www.houzz.com/discussions/need-screened-in-patio-advice-dsvw-vd~5253151) are better than the ones you have shown here, so I'd re-post those on this thread.

Some good advice here about mixing some of the new soil with the existing soil, when you add a raised bed. Also this article

I suggest your local library (old fashioned research, I know) and time spent browsing their many landscape books. You'll have so many ideas you will have to pick and choose. You appear to have both sun and soon-to-be shade, a good beginning, lots of room to be creative with. Lucky you!