It looks like nobody has volunteered information about building a thing like you describe.

I have not tried to make any combination worm composter/planters. Although the idea of combining functions "all-in-one" sounds appealing, I think the problem here is that the functions are not totally compatible.

Container plants need to be watered, in such a way that the soil drains freely and dries out to some extent before the next watering, otherwise the soil will be waterlogged and not have enough oxygen in it for root growth. Worm bins need to consistently stay within a certain range of moisture; not too wet and not too dry, but the range they need is generally much more wet than what container plants need.

Also, composting worms are not the same species of worms that live in and burrow through the soil. So they are not really ideally suited to burrow through soil in a container. That's why composting worm bins are filled with looser, more moisture-retaining and air-retaining materials like shredded paper and cardboard, not potting soil or garden soil.

I think it will generally be much easier to keep the right conditions in each if container plants and worm bins are kept in separate containers. It is not difficult to add worm castings/vermicompost to container plants by hand.

Charlie: does your planter has a bottom and what size? How much surface space are you willing to "sacrifice" for this composter? My suggestion will require digging. To sort of confine the worms, you could bury a nursery pot, with removed bottom (or not). If you live in an area with frost, the deeper pot you choose, the more frost protection it will provide.

A plus with charlie's idea, whatever mess you make while playing with the worms, you don't have to clean up. Just throw it back in the hole. No wiping, no sweeping, no vacuuming and no nagging.