How do you add the snap store to Synaptic?

You can't, today, do this.

Somebody would have to extend synaptic to talk to snapd, either directly or using snapd-glib. While relatively straightforward (and nearly everything the snap tool does is by talking to snapd), it is quite a lot of work, especially if (as I imagine is the case) synaptic has not been thought from the start to talk to multiple packaging backends.

Given that synaptic has seen no work in two years, and that the project maintainer is a very active snapd developer, I suspect development on it has stopped.