I wonder which way the wall faces? Partly envy, I would love a wall like that to grow something up, but more wondering how much light it takes? There are good reasons not to concrete land over, it looks like it will drain down to the wall for a start. Ecologically concrete is a real no, it produces a lot of carbon dioxide making concrete and it drains off into overstretched sewage systems and depletes the water table. What you have may seem like a small area, but small areas add up, people paving front gardens in suburbia to park cars have caused real problems some places. Gravel or pebbles would need weeding from time to time, but allow water through. I have a friend who has two small boys who are football mad and a very small back garden they turned to mud, he laid astro-turf, the water drains through it and from the house it looks just like grass. The ground cover/ shrubs option is a very good one.
Forty years ago when I was made redundant I made a living turning up and mowing such pieces for a minimal cost, I don't know how hungry people are in your neck of the woods, or if you can afford it, but the bit marked off is not large. I am curious, is the rest of the grass yours? Do you mow that? It does not seem much more, but the path has something of a municipal appearance to it.
And welcome to the forum.