You want to replace Slat __Slat Angle Control Control__ with Window __Window Shading Control Control__ in your second actuator (see below).

EnergyManagementSystem:Actuator,
  Window1_slat_angle,  !- Name
  Sub Surface 1,           !- Actuated Component Unique Name
  Window Shading Control,  !- Actuated Component Type
  Slat Angle;          !- Actuated Component Control Type

You can think of "Window Shading Control" as one category of actuators. Within that category, there are two control types -- Control Status or Slat Angle. __Slat Angle__. You're right that the documentation isn't great at explaining that, so what you can do is generate the EMS Data Dictionary (EDD) output file with detailed actuators options for your input file. This is done by adding an Output:EnergyManagementSystem object to your input file and setting the first input field for Actuator _Actuator Availability Dictionary Reporting Reporting_ to "Verbose". Save your input file, run a simulation, and EnergyPlus will generate the EDD output file for you to review actuator options.

UPDATE: __UPDATE: Adding more information about the EDD output file and specific solution to this problemproblem__

The Output:EnergyManagementSystem object has three input fields that each tell EnergyPlus how much information to generate in the EDD output file. The first input field is about EMS Actuators, but the two other input fields also relate to EMS Internal Variables and EMS Programs. From these three input fields, the EDD output file will have three sections (one related to each input field). The section related to EMS actuators begins with the following comment line:

! <EnergyManagementSystem:Actuator Available>, Component Unique Name, Component Type,  Control Type, Units

Everything between this line (line #30 in the EDD file you shared) and the next similar comment line for internal variables is a potential actuator you can use. Searching for "slat" doesn't appear anywhere in this EDD file, which means that the Slat Angle __Slat Angle__ actuator isn't available. This is weird, since it appears that you have set up everything correctly for the blind and window shading control. After some testing, I discovered that changing your window shading control's Type _Type of Slat Angle Control Control_ input field from FixedSlatAngle to ScheduledSlatAngle __FixedSlatAngle__ to __ScheduledSlatAngle__ (and then setting a schedule in the following input field) fixed the problem (updated input fields start with "*" below).

WindowShadingControl,
  Shading Control 1,       !- Name
  Thermal Zone 1,          !- Zone Name
  1,                       !- Shading Control Sequence Number
  ExteriorBlind,           !- Shading Type
  ,                        !- Construction with Shading Name
  AlwaysOn,                !- Shading Control Type
  Office Activity,         !- Schedule Name
  350,                     !- Setpoint {W/m2, W or deg C}
  Yes,                     !- Shading Control Is Scheduled
  No,                      !- Glare Control Is Active
  Window Material Blind 1, !- Shading Device Material Name
*      ScheduledSlatAngle,          !- Type of Slat Angle Control for Blinds
*      Always Off Discrete,                        !- Slat Angle Schedule Name
  ,                        !- Setpoint 2 {W/m2 or deg C}
  ,                        !- Daylighting Control Object Name
  Group,                   !- Multiple Surface Control Type
  Sub Surface 1,           !- Fenestration Surface 1 Name
  Sub Surface 2;           !- Fenestration Surface 2 Name

This is likely an issue with the EMS Application documentation (it should say "this slat angle EMS actuator only works for ScheduleSlatAngle control of blinds), but it could be a bug in EnergyPlus if the developers expected the actuator to work with blinds for all situations.

There are a few other fixes to make in your EMS program, so I'll email you my updated input file with more details.

You want to replace __Slat Angle Control__ with __Window Shading Control__ in your second actuator (see below).

EnergyManagementSystem:Actuator,
  Window1_slat_angle,  !- Name
  Sub Surface 1,           !- Actuated Component Unique Name
  Window Shading Control,  !- Actuated Component Type
  Slat Angle;          !- Actuated Component Control Type

You can think of "Window Shading Control" as one category of actuators. Within that category, there are two control types -- Control Status or __Slat Angle__. You're right that the documentation isn't great at explaining that, so what you can do is generate the EMS Data Dictionary (EDD) output file with detailed actuators options for your input file. This is done by adding an Output:EnergyManagementSystem object to your input file and setting the first input field for _Actuator Availability Dictionary Reporting_ to "Verbose". Save your input file, run a simulation, and EnergyPlus will generate the EDD output file for you to review actuator options.

! <EnergyManagementSystem:Actuator Available>, Component Unique Name, Component Type,  Control Type, Units

WindowShadingControl,
  Shading Control 1,       !- Name
  Thermal Zone 1,          !- Zone Name
  1,                       !- Shading Control Sequence Number
  ExteriorBlind,           !- Shading Type
  ,                        !- Construction with Shading Name
  AlwaysOn,                !- Shading Control Type
  Office Activity,         !- Schedule Name
  350,                     !- Setpoint {W/m2, W or deg C}
  Yes,                     !- Shading Control Is Scheduled
  No,                      !- Glare Control Is Active
  Window Material Blind 1, !- Shading Device Material Name
*      ScheduledSlatAngle,          !- Type of Slat Angle Control for Blinds
*      Always Off Discrete,                        !- Slat Angle Schedule Name
  ,                        !- Setpoint 2 {W/m2 or deg C}
  ,                        !- Daylighting Control Object Name
  Group,                   !- Multiple Surface Control Type
  Sub Surface 1,           !- Fenestration Surface 1 Name
  Sub Surface 2;           !- Fenestration Surface 2 Name