I am not quite sure what that last message is meant to convey, the screen cast of the QT dialog. But I guess you have troubles with our message system? Please post your code in the future, it is not fun to write boilerplate code for user issues.

Cheers,
Ferdinand

Explanation

File: test.c4d

Code

Script Manager Script:

import c4d

doc: c4d.documents.BaseDocument  # The currently active document.
op: c4d.BaseObject | None  # The primary selected object in `doc`. Can be `None`.

# ID of the first user data element (a button).
ID_BTN_1: c4d.DescID = c4d.DescID(c4d.DescLevel(c4d.ID_USERDATA), c4d.DescLevel(1))

# ID and fields for our custom message.
ID_CUSTOM_MESSAGE: int = 1065587  # Registered as a plugin ID under developers.maxon.net
ID_CUSTOM_MESSAGE_TARGET: int = 0 # Made up IDs for the container fields.
ID_CUSTOM_MESSAGE_DATA: int = 1   # Made up IDs for the container fields.

def main() -> None:
    """Called by Cinema 4D when the script is being executed.
    """
    # Send a message to a singular node.
    op.Message(c4d.MSG_DESCRIPTION_COMMAND, {"id": ID_BTN_1})
    
    # Broadcast a message to multiple nodes, here we broadcast into the document node, i.e., 
    # all nodes in the document in this case. When we would send this to an object, it would be
    # broadcasted to all children, tags, tracks, curves, etc of that object.
    doc.MultiMessage(c4d.MULTIMSG_ROUTE_BROADCAST, c4d.MSG_DESCRIPTION_COMMAND, {"id": ID_BTN_1})

    # But for buttons we implement ourself it is a bit nonsensical to simulate a button click, as
    # we then also can just implement any other message. Here we send a quasi-custom message type
    # via #MSG_BASECONTAINER as we cannot implement truly custom messages in Python.

    # Create a container and mark it with our plugin ID so recipients can identify it. Then mark 
    # the message as targeted at tags, add a payload, and broadcast it into the document.
    bc: c4d.BaseContainer = c4d.BaseContainer(ID_CUSTOM_MESSAGE)
    
    bc.SetInt32(ID_CUSTOM_MESSAGE_TARGET, c4d.Tbase) # Could also pass Tphong, to only target phong tags for example.
    bc.SetString(ID_CUSTOM_MESSAGE_DATA, "Hello World")
    
    doc.MultiMessage(c4d.MULTIMSG_ROUTE_BROADCAST, c4d.MSG_BASECONTAINER, bc)


if __name__ == '__main__':
    main()

Python Tag:

import c4d
import typing

doc: c4d.documents.BaseDocument  # The document containing this field object.
op: c4d.BaseTag # The Python tag containing this code.

# ID of the first user data element (a button).
ID_BTN_1: c4d.DescID = c4d.DescID(c4d.DescLevel(c4d.ID_USERDATA), c4d.DescLevel(1))

# ID and fields for our custom message.
ID_CUSTOM_MESSAGE: int = 1065587  # Registered as a plugin ID under developers.maxon.net
ID_CUSTOM_MESSAGE_TARGET: int = 0 # Made up IDs for the container fields.
ID_CUSTOM_MESSAGE_DATA: int = 1   # Made up IDs for the container fields.

def main() -> None:
    """Called by Cinema 4D to execute the tag.
    """
    pass

def message(mid: int, data: typing.Any) -> bool:
    """Called by Cinema 4D to handle messages sent to the Python Generator object.
    """
    # Handle a direct button click message. What you did in your code, just testing for the ID 1 in
    # the second desc level, is not so good, as your code could would then also trigger for buttons 
    # located in other sub-containers with the ID 1. You should test for level 0 being of value
    # c4d.ID_USERDATA and level 1 being of value 1. You also do not test for the sent DescID having
    # two levels in the first place, which would lead to errors when there is a button in the top
    # level of the description and the user clicks it.
    if mid == c4d.MSG_DESCRIPTION_COMMAND:
        isBtn1: bool = isinstance(data, dict) and data.get("id", c4d.DescID()) == ID_BTN_1
        if isBtn1:
            print (f"Button 1 pressed on node: {op.GetName()}")
        
        # We could also write it in this form, I find my variant a bit cleaner.
        # did: c4d.DescID = data.get("id", c4d.DescID())
        # if did.GetDepth() == 2 and did[0].id == c4d.ID_USERDATA and did[1].id == 1:
        #     print (f"Button 1 pressed on node: {op.GetName()}")

    # Handle a container message with which we can send a broad range of data, we check that the
    # container is marked with our custom ID.
    if mid == c4d.MSG_BASECONTAINER and isinstance(data, c4d.BaseContainer) and data.GetId() == ID_CUSTOM_MESSAGE:
            # Check that the type of this node is an instance of the target set in the sent container.
            if op.IsInstanceOf(data.GetInt32(ID_CUSTOM_MESSAGE_TARGET)):
                print(f"Custom message received with data: {data.GetString(ID_CUSTOM_MESSAGE_DATA)} in node: {op.GetName()}")

    return True
```

Thank you for reaching out to us. The answer depends on where the button is located. Button in dialogs cannot be clicked programmatically, unless you own the implementation. Buttons in descriptions can be clicked programmatically, i.e., descriptions means things that live in the Attribute Manager. An easy way to do this is c4d.CallButton.

Where this rule is somewhat broken, is when a button embedded in the UI of a paramater. E.g., a button in the flyout of a Color field. The button must be its own entity with its own ID, so that you can call it.

Cheers,
Ferdinand