The main effect of diet is that more muscle can slightly increase your BMR, and the other health benefits of being in shape. It does also increase calorie loss from activity at the margins, even if it's a pretty small effect. (maybe 100-200 more per day etc in my experience.)
None of this will help much without the diet, but it's not useless.
Muscle and fat are metabolically active, which means they burn calories just to stay alive. If you lose fat, guess what? Your body doesn’t need as many calories to survive.
Another factor is the calories you burn not exercising. We burn calories all day, even when we’re not exercising but when people are dieting they tend to have lower energy so the don’t move around as much.
So yes, technically metabolical rate slows down but it’s not some conspiracy against you. It’s a direct result of losing fat.
That’s why some people lift weights while dieting to build muscle at the same time they’re losing fat. Personally, I haven’t had a huge issue with caloric restriction so I’m doing a more intense diet in the short term, then cooling off once I get to my goal weight and switching to more weigh lifting.
I would like to add that exercise also helps you to influence where you lose weight. Your body will often choose to lose muscle mass when you are running a calorie deficit. If you lift weights you are stimulating muscle growth which helps to shift your body to lose weight through fat loss.
That's certainly part of it (and people should absolutely exercise, regardless of their weight/metabolic/body fat goals, to be clear) but my understanding is that your immune system also reduces its activity level after increasing your level of physical activity, reducing caloric expenditures, as do a few other bodily systems
The only consistent way to enter a caloric deficit is to diet, which is very hard for the obvious reasons