With such a steep slope in a short distance, you would be looking at major, major expense to push back and rebuild a fully engineered retaining wall. Okay -- more than I would be willing to spend to add a room. There are also setbacks and building codes to consider. It might be cheaper to add a second story to the house. Or rent studio space somewhere else. Or sell and buy a different house that meets your needs.

"Can I push back the retaining wall without compromising safety?" Probably not within a reasonable cost. The wall height and the short horizontal distance doesn't lend itself to inexpensive modifications as kiminpl said.

"I like the idea of having terraces with beautiful plants." Where are you? What will work specifically will vary with where you are. You most likely don't want to use plants that will require irrigation since water and walls may not be a good thing if it wasn't initially built well. Working much in this type of a sloped area can be difficult, so you don't want to use plants that require a lot of maintenance such as pruning, deadheading, and weeding, though some attention will be needed. You already have trees there so I am not sure that you will be able to do any further terracing without losing the trees. You may need to call in an engineer to evaluate the wall stability if you will be moving the soil into terraces as I don't see any evidence that the wall is properly tied back into the hill rather than just built across, so I would be hesitant to change the stresses without an evaluation of its stability.

In my area (northern New England), I would put down a layer of cardboard and a highly textured mulch such as shredded bark ("gorilla hair") or utility line trimmings, and leave it for a year. Any weeds that came up through the mulch I would use glyphosate on. With a clean slate I would then plant relatively small shrubs and a groundcover to provide an evergreen background, keeping in mind foliage color and texture as well as flowers, berries, and autumn foliage color. At least some plants would need to be evergreen or have other winter ornamental value such as brightly colored stems or berries since winters here are long and stark. Whether this would work near you or if a different type of plan would work better, I can't tell from information given. Just keep in mind that less is more in this type of planting as far as number of types of plants in order to keep maintenance to a minimum, and bare soil will grow weeds (more maintenance), so you want as little bare soil as is possible.

What have your neighbors done with their yards since at least some must have similar slopes?