How to anchor Essential Graphics template to corner?

MOGRTs, Essential Graphics, do not have any way I know of to determine the size of the Sequence they are used in. You can determine the size of a comp in After Effects, but you cannot have an expression or script look at the frame size in Premiere Pro.

To solve the problem, I usually create a drop-down menu based on frame size that moves the graphic around. My usual list looks like this:

1. 4K
2. HD
3. Social Square
4. Social Portrait

The position and size (scale) of all of the elements in the scene are tied to if/else arguments that specify where they go and what the size is when the end user picks the frame size using the menu. I created a Shape layer with multiple rectangles and set it as a guide layer to help with positioning in After Effects. It's a pretty straightforward workflow, and the AE project looks something like this:

The Comp is 4K because that's the maximum frame size for this client. The Comp uses a simple Control Null to control the position and scale of the Name and Subtitle layers as well as the matte for the Subtitle. Here are the expressions:

// POSITION
frmSize = effect("Size Master")("Menu");
frmAdj = effect("Master Position")("Point");
if (frmSize == 1){
	value + frmAdj;
}
if (frmSize == 2){
	value + frmAdj + [324, 10];
}
if (frmSize == 3){
	value + frmAdj + [324, 350];
}
else if (frmSize == 4){
	value + frmAdj + [-760, 520];
}

// SCALE
frmAdj = effect("Master Scale")("Slider");
frmSize = effect("Size Master")("Menu");
if (frmSize == 1){
	s = frmAdj - 25;
}
if (frmSize == 2){
	s = frmAdj - 50;
}
if (frmSize == 3){
	s = frmAdj - 50;
}
else if (frmSize == 4){
	s = frmAdj;
}
value + [s, s]

That should get you started.