Cardinals do have 7 picks. They have their own pick in each round. They got a compensation pick for losing Marcell Ozuna OF to the Braves. I don't like it either but they do get that Competitive Balance pick each year. This year they traded their Competitive Balance pick in Round A to the Rays but got the Rays Competitive Balance pick in Round B back in the deal.
Giants also have 7 picks (13, 49, 67, 68, 85, 114, 144).
In the Division
Braves (25, 97, 126, 156)
Mets (19, 52, 69, 91, 120, 150)
Marlins (3, 40, 61, 75, 104, 134)
Nationals (22, 55, 71, 94, 123, 153)
PHILLIES (15, 87, 116, 146)