Ground cover = Ajuga... upright = hosta... Flowering Impatients

No seeds that you can spread will do well in shade. Besides shade you have to consider what will do well competing with your tree roots too. There are a few plants you can buy that will do well. I second the hosta. It comes in lots of different heights and colored leaves and flowers. Don't pack it full because they grow fast. If you know someone who has some well established ones ask for a piece or 2 for next spring. I'm always happy to share pieces of mine.

For ground cover I suggest Golden Creeping Jenny Moneywort. It's bright gold color really pops in the shade. Unlike many groundcovers it is easy to pull off tendrils so it doesn't become invasive. You don't need many plants either because 1 plant will cover 2 or 3 feet in one season. While Impatiens are gorgeous they don't do well competing with tree roots

Ferns would work too.

I just planted white astilbes in a shady area. Very, very pretty with ferns and hostas.

You could try some foxglove and columbine seeds.

I'd also put some spring bulbs in there, for sure. :)

Just came across your old post when searching for info on growing astilbe from seed... I am curious as to what you decided to do and what the area looks like now,a year and a half later.

I must say your honeysuckle seems to be the alien invasive Amur honeysuckle, an insidious shrub that unfortunately bordered the rear flowerbeds in my backyard when we moved here 3 years ago. This year I finally persuaded my neighbor to cut them all down, so I only should have to do battle (in my vegetable AND flower beds AND the lawn) for another few years with the germinating seeds pooped out by the birds from thousands of "yummy" red berries all over my 1.3 acres.
In addition to the 5-6 full-grown honeysuckles along the property line, there were about a dozen of these monsters on our property that the previous occupants had kept pruned back into low (4-6') bushes. I cut every single one to the ground and carefully painted each remaining stump-end with a good, strong shrub-killer (the only time in my 40+ years as an organic gardener I ever have resorted to an herbicide--just shows you how much I detest honeysuckle). I laboriously dug out half of them a month or so later, but found by waiting another year, the other roots gave me less of a battle as they had partially rotted.
I think you would have a much nicer little garden spot if you were to remove the honeysuckle and instead plant a nice little native tree such as a redbud or dogwood. This would still provide some dappled shade and any bulbs or perennials (or part-shade-tolerant annuals) would thrive as opposed to a few plants merely surviving, which is, I am certain, all you would have as things are.

Please post a new photo if you have one!