I don't think the lawn needs any more shade so I'm thinking dwarf red Japanese maples in accent colors here and there. And ferns in gold and lime green.

Well, as a general rule, ALL flowers attract bees. Whether they are regular growing-in-the-ground-or-pots flowers or flowering shrubs or trees.

You will likely need a local designer to figure things out because, well, there needs to be a design. You could start more think by making a rough, sorta to scale drawing of the actual property and try the “ bubble diagram “ method to identify play areas ( you mentioned not wanting things near play areas, but where are they?) , areas that should bd left as lawn, what areas you “ see” most from inside, or any outdoor sitting areas. What is the property belongs fence ( plantable, or not). It would be help if you know what areas, or a few of them, get the most sun & how much.

I like tracefloyd’s preliminary suggestion because it’s in line with your list. You might like a fairly traditional, not- very native but simple SC landscape of a few JM’s, some small azaleas ( the reblooming types like some sun though), ferns & hostas. And what’s your actual zone, how hot— several JM cultivars can take a lot more heat.
A lot depends on how far away you are viewing from. By “ welcoming” did you mean drawing you out into the yard? That is where a good design comes in, as to where to plant & where you will walk. Foliage that contrasts well with lawn, by leaf size or colors, can work well closer up. If you’re planting something at the end of a long narrow yard, not in the middle it, you might have room for a dogwood or such. In your photo there appears to be a reddish foliaged tree in the distance - neighbor’s?

littlebug is correct about flowers and bees, though some are more bee- magnets than others, plus different bloom times can relate to when you’re in the yard more or less, so you’ll have to think how all that works for your family, or again, what areas are for what.

Needlepoint ivy grows fairly slowly and can be controlled. Variegated yellow, cream and green growing in a few places on the iron fence.