Connie is a lovely lady corgi. I find your choice of descriptive words of Connie's before re-homing life very telling of some personal bias. There are some corgis that simply just don't play and some that could care less about having social relationships with other dogs. They may not see themselves as "canine" but as people and prefer relationships and bonds with their "equals" over canine "friendships." From much of what you've written about Connie, I'd say she fits into preferring people to canines, is a very clever and bright dog and certainly has the number of many of the humans she associates with.
Debbie