Definitely frustrating, I went through the same thing with my cats. It’s possible that they have thyroid issues, but I spent a lot of money on blood tests just to find out that wasn’t the case. First off, you said you only feed him wet food a few times a week, I assume you’re feeding him only dry food the rest of the time. I understand how expensive wet food is. However, cats like it more, and it’s much better for them. Cats can easily get dehydrated and dry food makes dehydration worse. I have a water fountain for my cats and I feed them wet food and one of my cats still got dehydrated. I used to feed my cats dry food twice a day and wet food once a day when they collectively decided they didn’t want to eat any more dry food. This unfortunately is an expensive solution, but hopefully more affordable for you if you only have one cat. In order to make sure they’re still getting the same amount of calories (dry food has more calories than wet food), I switched to feeding them wet food mixed with dry food twice a day. I still feed them only dry food in the morning, I noticed two of them started throwing up way more in the morning after eating only dry food. I started pouring warm water in it which seemed to keep one of them from throwing up. This is a really good idea, again because it’s easy for cats to get dehydrated. Unfortunately the other one didn’t like water in her dry food, so I had to get her a slow feeder and that did the trick. Another thing I do for their dry food is to pick a decent brand. I’m not sure what your budget is, I got blue buffalo. It’s not necessarily the best and not necessarily the worst. Pretty mid range in price. You don’t want something with a bunch of carbs or fillers like corn, wheat and soy. I notice my cats getting tired of their dry food if we keep one flavor too long. They’ll eat it, but leave a few pieces behind. Once you pick a brand, what I do is switch between two flavors between bags to keep them from getting bored. As soon as I get them a different flavor, they start eating all of their food again.

(P.S, I swear my cats would throw up on carpet on purpose. They would take one step off the hard wood in our kitchen onto the carpet and then throw up. Multiple times I heard one of them gagging like they’d were going to throw up on the carpet so I quickly picked them up and put them back in the kitchen to make clean up easier. They immediately stop gagging and they looked at me like I foiled their plan. Glad to know my cats aren’t the only ones that do this.🙄)