I've seen the traditional gravity chairs. When you said it might have looked like a hammock. I searched with that term and found this: https://www.sharperimage.com/si/view/product/The+Zero+Gravity+Hammock+Chair/201444
Also if your head was slightly raised you could try a wedge like this one under your mattress. Some people with POTS and orthostatic intolerance get a little relief by sleeping with the head elevated or so I've read. It did not help me but my mom uses one by Avana on her bed to help with breathing for her COPD.
Note that they do off gas quite a bit for a few weeks if you have MCS (multiple chemical sensitivities) like we do.
Honestly I wish I knew what it looked like; ended up looking at pictures of my old dorm but unfortunately I don't see them outside anymore. I think their recline was a bit similar to what you posted, except it has a bit of a mellower, slightly flatter angle.
I think I might experimentally try DIYing my own wedge (my mattress is a brick anyway, anything would lift it up); 3 nights with my head lifted up, and 3 nights with my head lifted down so I'll be able to check out what blood rushing to my head does, like another member suggested. It's still an interesting idea and even if nothing much happens I think it'd still be good data on the POTS thing.