One way to determine a team's farm system success is by looking at its roster construction. Fangraphs' Roster Resource has a great page to see the makeup of each MLB team. I would recommend spending time on this website to learn more about the various teams. Unsurprisingly, the majority of teams are made up of "homegrown" players from their own farm systems with trades being a close second. Let's take a look at the Cardinals' 40-man roster makeup.
St. Louis Cardinals
The roster is primarily made up of "homegrown" players. This places them in the upper quarter of teams with homegrown talent (the Astros, Twins, White Sox, Guardians, Dodgers, and Royals). Having homegrown players on your roster doesn't automatically make your farm system one of the best, as is shown by the list of teams with the Cardinals. However, it is a strong indicator of how successful your team is at promoting players.