Is there a way to add a socket of a specific type to group nodes? Currently, it seems that they default to grey scalar sockets, and I don't see any way to change their type.
You need to connect the temporary socket (red) to the values you want to make available from outside the group.
When tab out of the group you will have all of them available for wiring with the correct type (indicated bei their color).
Note that you can't edit them later you would need to recreate the group.