You don't need to add anything for edging. You can just cut a crisp, sharp edge with a spade or edger. But I would strongly urge you to remove the landscape fabric before it's too late.

Why do I need to remove the landscape fabric?

Because plants will root through it and weeds will grow on top. It will not keep down weeds long term and will be a really tough job to remove when, as is almost inevitable, it becomes an infested mess. Also it's a barrier to soil cultivation and planting and will eventually degrade in the soil, polluting it with inorganic matter.

The disadvantages of landscape fabric | Good Growing | Illinois Extension | Illinois https://share.google/KQn6Vl6YAd9y7ZGGC

What floral said above. 👆

Landscape fabric is evil.

You have a high fence, so bushes for privacy wouldn’t be necessary. Clean up the edge and see if you can get new grass to grow there. If you have children (the trampoline seems to say you do) then more landscape work at the edge of your property isn’t necessary.