From what I could find
MLB official scorers are technically league-appointed independent contractors rather than direct, full-time employees of an MLB club or the league office in the traditional sense.
Here is how the system works:
League Appointment: Since 1980, Major League Baseball has centralized the appointment of official scorers. This was done specifically to eliminate the conflicts of interest that existed when local newspaper beat writers (who were often cozy with the home team) performed the role.
Local Assignment: While they are appointed by the league to ensure impartiality, they are effectively "local" in the sense that they are assigned to a specific stadium for the season. Unlike umpires, they do not travel with teams. Most official scorers live in or near the city where they work.
Backgrounds: They are typically individuals with deep baseball knowledge—often retired sportswriters, former coaches, umpires, or people with extensive experience in professional or amateur baseball scoring.
Professionalization: Because their decisions (such as "hit vs. error") directly impact player statistics, contract bonuses, and league records, the process is highly standardized. Scorers have access to instant replay video and are in constant communication with the MLB stats department in New York throughout the game.
In short, they are independent experts selected and overseen by the league to maintain neutrality, though they usually reside in the local market of the stadium where they are assigned.