If the wall on the left gets sun in the morning time, then the exposure is something like south-south-east, so rather shady.
If shade is open to the sky it is usually considered to be bright shade, but as tree cover encroaches the shade becomes deeper, and even more so with a building overhang. The area that does get some morning sun will be the best spot, even for most shade plants.
Another, area to consider is the in-ground space immediately in front of the entrance porch to each side, next to those low lanterns. A planting there of low shrubs could soften the lines of the entryway, perhaps Camellia, Sarcococca, or Aucuba japonica.
Low Camellia sasanqua and Hosta would be a fine combination for those spots. When the Hosta die down in Winter, interest would shift to the Winter blossoms of the Camellia.
Heuchera cultivars are also fine shade plants that provide foliage color and pattern, even in full shade conditions.
Unlike the other plants I mentioned, they are not traditionally used in Japanese gardens, but could work well in one all the same.
