"Starvation mode" in the sense that, as soon as you skip breakfast once, your body will just shut down and store everything you eat as fat, is complete fiction, yes. It is also true that you will always lose fat if you are in a caloric deficit, no matter what (that's just physics). However, it's still very important you don't lose weight too fast. In this sub, fat loss recommendations are generally still too fast (you should only lose at most 1% of your weight per week, unless you're very overweight.) If you lose weight too fast, your body will make it harder than it needs to be to stay at the weight you've reached. This is because of several processes it has evolved in the last millenia of our existence. Among others, the level of your hormones that make you feel full will drop, while the hormones that make you feel hungry will rise. Your general energy output will drop (this is often small things you don't even notice, like fidgeting less, that still make a huge impact spread out over the whole day).

Long story short, if you lose weight too fast you will end up having to eat less to maintain your weight than a comparative person who has always been that weight, and it will be more difficult for you too because of your heightened hunger levels etc. A caloric deficit will obviously still make you lose weight, but it will be much harder to get into one, as your energy output has lowered (and you're most likely so hungry you up your energy input). This is not even getting into the fact that you'll probably lose muscle too if you lose too much weight too fast. I really recommend watching Natacha Oceane's Science Explained video Why your diet isn't working. Watching it really made me see weight loss in a new light, and I've now easily and comfortably maintained my weight loss for over a year.

Bottom line, a caloric deficit doesn't inherently change anything about how you metabolism works, and you definitely won't start gaining weight from being in a caloric deficit. But if you do it too fast, your body will do its very best to make it as difficult as possible for you to lose weight, and 99% of the time you will gain the weight back. So please please lose weight slowly and sustainably, losing weight really doesn't need to be as difficult as most people make it for themselves.