In order to execute the script automatically when Agisoft Metashape Professional instance is run you need to place Python script to the following folder:

on Windows:

   C:/Users/<username>/AppData/Local/Agisoft/Metashape Pro/scripts/

on Linux: 

   /home/<username>/.local/share/Agisoft/Metashape Pro/scripts/

on macOS: 

   /Users/<username>/Library/Application Support/Agisoft/Metashape Pro/scripts/

on any OS (for all users):

   <installation folder>/scripts/

Usually, such autorun scripts are useful for adding custom menu options to call the custom processing operations directly from the application GUI instead of using Run Script dialog each time.