So, this is quite easy but you might want to be patient with this one as we have cloth sims and they are hectic. Sorry but geometry nodes won't work. So to make the pillow as you want. Add a plane, scale it down to the size of the pillow, go to edit mode, and subdivide it 10 times. Now, slightly extrude up the upper part, but very slightly. Then, go to select on top, select sharp edges, and on the top right enable merge, the option near the XYZ and butterfly thingy. Then press S to scale, press Z, and then press 0 to smash the thing.
Now, it has become one edge. Now, for the part which will torture your computer, er... I mean fun stuff. Go to the physics panel and click on cloth. There, enable pressure and set the pressure to 5. Then, if the cushion is landing on anything, enable collisions on the object it will land on. If you run the sim, you will see the cushion is low res. SO add a subdivision modifier and set it above the cloth modifier. Not doing so will change your life for the worse. There, set the viewport amount to 2.
Now in physics properties, go to physical properties and set it to 0.01. You can decrease it more if you want it to be fluffier or increase it to be less fluffy, your choice. Now, to remove that huge gap, go to object collisions in the cloth settings of the cushion and set it to 0.001. Then go to soft body and cloth and set Thickness Outer to 0.001. Then go to the quality of the collisions and set it to 10 for a higher quality collision. If you want to slow down the speed of the falling, you can always increase the pressure. Now, set the cloth simulation quality to 10 if you see some issues. Then, first, apply the subsurface and then the cloth modifier. Do it in this order or you will have a bad time. Now, again add a subsurface modifier after applying the previous 2. Then, right-click on the pillow and shade smooth to give it a beautiful look.
BTW here's the video link if you want:
As for the finger effect, like the pressing thingy, you can always use force fields for that.