This is a common pattern and one of the reasons that crash diets don't work in the long run.

I've struggled with the same issue as you and started really digging into the science of food and nutrition because I've had enough of yo-yo'ing.

Fat storage is regulated by various hormones. The most significant are insulin, cortisol, testosterone, estrogen and hormone-sensitive lipase. Hunger is caused by the release of the hormone gherelin.

The way to lose weight and keep it off permanently is to make permanent lifestyle changes that hack these hormones.

The first part is to drastically lower the production of hormones that trigger fat storage. Insulin seems to be by far the most significant. The best way to drastically lower insulin is to not eat, but the next best thing you can do (because not eating isn't really all that practical for most people) is to severely restrict carbohydrates. This means all carbohydrates, including those from fruits and vegetables. You mentioned lots of vegetables, including carrots - well, carrots are an extremely high-carbohydrate vegetable, they're almost like eating sugar. They'll give you an insulin boost and you'll feel hungry again very shortly after eating them. We've been duped by being told that "fruits and vegetables are good for us." The reality is way more complicated than that.

Cortisol is the stress hormone. While I don't buy claims that exercise results in weight loss (because I used to jog for an hour every single day, never ate junk food and was on a "well balanced" diet recommended by all the leading authorities and was still obese and couldn't lose weight) but exercise is great at reducing stress, and so it can help with weight loss ... just not as much as diet. Other ways to keep cortisol low are to make sure you're getting enough sleep and obviously reduce stressors in your life.

Testosterone and estrogen can also be regulated somewhat by exercise, as well as nutrition.

As for gherelin, there's good news and bad news. The bad news is that gherlin is released by your fat cells when they start to deplete. It's your body's way of saying "I'm using stored energy, we better find some more." But the good news is that it seems to be temporary and insulin seems to be a factor here too.

When you eat, your body releases insulin to moderate the influx of new blood sugar. Your fat cells get a boost of new fat storage and the release of gherelin is suppressed. But as soon as your blood sugar levels come down and those fat cells start to empty rather than fill you get a new release of gherelin which makes you want to eat so you rinse and repeat. And people who get into a cycle of weight gain become resistant to both insulin and gherelin ... so your pancreas and your fat cells keep releasing more and more just to produce the same effect and a vicious cycle ensues and this is how people become morbidly obese.

So by drastically reducing your insulin levels by cutting carbs, intermittent fasting and filling up healthy fats ("unhealthy fats" like poly-unsaturated fatty acids; PUFAs have their own health problems associated with them) you cut off the production fat-storing hormones and you limit hunger hormone. Then you can restrict calories and not torture yourself. This doesn't mean that you won't ever feel hungry, gherelin production won't stop ... but it will lower and become temporary. You'll find yourself feeling hungry at certain points in the day but it goes away after a few minutes without eating anything.

Long term, once you've cut the weight, you can go back to eating more calories, but by changing your diet to consume very few carbs and to eat less in general (typically by eating once or twice per day) you keep insulin levels very low. The result is that you get the energy your body requires but it's using it rather than storing it as fat and you're not feeling hungry all the time. And you're much more likely to make a change permanently if it's comfortable and not torturing you.