You’ve described very difficult conditions for the establishment and continued growth of plants that would provide the kind of services you’re looking for. I can’t think of any plant(s) that provides a high probability of success. Asian honeysuckles produce chemicals that suppress competition (allelochemicals), so the honeysuckle would need to be removed before you plant anything. A plan would need to be in place to prevent honeysuckle from re-establishing from seed.

However, the extreme slope at 45 deg. slope presents a considerable challenge. Most likely, the oak roots and honeysuckle are currently keeping the soil from sloughing off. Once the honeysuckle is removed, you could lose a lot of soil down-slope.

Normally, grasses and sedges would be a good choice given that they produce thick root systems and would be good competitors against juvenile honeysuckle. However, our native grasses require full sun. Don’t believe everything you read about “shade-tolerant” grasses; our grasses didn’t evolve in forests. Shade tolerance is one reason we see some non-native grasses being used on shaded slopes. However, the highly invasive Japanese stiltgrass (Microstegium vimineum) provides a cautionary tale. It was introduced into the U.S. partially for use on shady forest slopes but is now spreading unchecked in many of our forests. Some sedges can grow in shade, but they typically require consistent watering.

Some sumacs are shade tolerant. For example, fragrant sumac (Rhus aromatica) is commonly used on forest slopes as long as there’s some filtered sunlight. As its name implies, grow-low sumac (R. aromatica 'Gro-Low') produces a dense canopy close to the ground. However, keep in mind that plant establishment could be hampered by dense shading, so it may take a long time for the planting to provide the kind of benefits you’re looking for. Also, you will need to water the newly planted sumac. Of course, this would be true of any new planting.