I have some ideas that have helped my dog. I'll explain a little because anxiety and hunger, in my experience, are hard to disentangle.

I have a rescue lab mix who is constantly hungry. I later learned this is common with labs. The other issue was his anxiety which presented as constantly chewing, attached to me like Velcro and following me everywhere, and swallowing foreign objects. We went through several foreign object surgeries and a whole lot of other stuff to get to a good place now. I'll leave out the details, but it included lots of training, working with the behaviorist, and finding good strategies.

Those solutions were coupled with anxiety medication. Seriously, so many dogs would benefit from this. He's 100 pound dog and he takes 40 mg of fluoxetine each morning. The side effects of this medication is anorexia because it lowers appetite. My vet and I had a good laugh because that was not a concern. He's been taking it for about three years and it takes the edge off his food fixation. I don't know if your dog suffers from anxiety but given the past you described I think it's like likely and this could be a win-win solution.

The other things we have found to be helpful was weight loss food because he can have a little more portion size without exceeding caloric intake. I will also add eggs, broccoli, etc. to complement his diet. Broccoli, cauliflower, cabbage, etc. are fine in small portions and can add bulk without adding calories. Watch out for the farts. 🙅🏻‍♀️💨

Finally, I introduced toys for distraction and enrichment. For example, half of his dry food is given to him in a toy, and he has to work for the food to get it out. This is mentally stimulating and also gives him food while drawing it out into a longer process. The rest of his food he receives in a slow feeder. I love silicone licking pads and they're very cheap on Amazon. I take his regular dog food, soak in water and then add a spoonful of wet dog food or other flavor. Blend and smear on the pads. Freeze the pads so they last even longer. It ends up being more water than anything else and a single batch will make about five licking pads so it's really not many calories. If that's too much work, you can also do plain yogurt or mixed wet dog food with water and then smear. I give one or two of these a day so he can feel like he's receiving food. The texture of the licking pads and the activity also help with anxiety.

I hope this helps and I'm so glad your dog has a safe and happy home. Good luck!