It’s better to ask for Motion help in the Motion forum, but I’ll see what I can do. The version I’m using here is older but the idea is the same.
I made a 3-d camera, then used the rectangle tool to make a white panel, duplicated it, colored the second panel gray just so you can tell them apart. The 2 panels are all in one master group so far, (see image)

I dragged the gray one off the top of the white one and put it edge to edge with it.

Near the top left are some options for the cursor: hover/press the cursor until you get the circle with round dot. This tool moves the “hinge point” or center of rotation, to where you need it, from the default place in the center of the rectangle, over to the edge, where it would look like a fold in a single sheet of paper, if both panels were the same color/texture. Use the colored arrows to place that hinge point right at the joint.

Once it’s in place, select the gray rectangle, go over to the Inspector on the left side, find the rotation controls for X,Y and Z rotation, and see how you can now make the card seem to flap open and closed. This is keyframeable

Finally, collapse the two rectangles into their group, highlight the Group, and try rotating and moving the pieces as a unit. This is the fundamental concept behind how I would do your greeting card effects. Besides coloring the rectangles, you’d apply your text to them, and the text effects. You see only two rectangles here, but I would have made four identical ones: because your completed card has four faces. So I would make 4 sub-groups to “weld” two faces back-to-back in each of two groups, then connect the two groups by hinging one to the other, using the overall master Group, containing all the others, to manipulate the complete structure.

That’s a quick-and-dirty explanation. Hope it helps.