So I’m 3 days post op on full liquid diet. Nausea and gas pains are mostly gone and I am able to drink a good amount of water.
I find myself hungry and full at the same time. It makes sense - my body is experiencing fullness in my stomach and hunger because I’m consuming less than 500 cals a day.
my question is - do those feelings sync up? Or will I always be plagued by hunger while my stomach tells me no?

The first few weeks after surgery are pretty miserable. Your body has been put through a huge shock, and is adjusting. You're all swollen and healing. Things definitely do settle down within the first few weeks or months, and it will get way, way easier.

One issue is that your stomach starts out really swollen - its capacity may be only 1/4 cup now, even though it may be more like 1 cup after the swelling has gone down. This makes it hard to even fit enough water and/or food in right now. Later you will be able to eat/drink more at a sitting, and you will start to feel more satisfied.

Another problem is that it is particularly difficult to get enough protein in at first, especially on the liquid diet. And yet your protein needs have actually gone up, because protein is essential for healing.

For me, the first couple of weeks on the liquid stage were absolutely miserable, and I was starving all the time, even though I also felt full and couldn't consume much. This went away completely once I moved on to real food and started to get enough protein in, and also because the swelling went down and it was easier to even do things like drink my water.

It could also be head hunger vs actual hunger. It takes a bit for your body to learn the difference with the restrictions.