curious, is it true pregnant women burn 300 extra cal?

300 cals per day equates to only between 2 and 3 lbs of fat gain per month so over the second and third trimesters this is only 12 to 18 lbs gain.

There are various factors as to why the extra calories are required.

The baby obviously needs energy and nutrients to grow. Yes it comes from the mother but the mother needs to replace energy and nutrients herself.

Also, being heavier increases BMR slightly so the mother's resting energy requirement will slightly increase simply because she is carrying more weight.

Obviously if someone is overweight then chances are they have enough energy reserves to support the growing baby without extra calories but for anyone of a healthy weight, extra calories are required.

In addition to weight gained due to the placenta, baby, etc, women are supposed to gain some fat during pregnancy, this is to support lactation. The female body undergoes various changes to support both pregnancy and lactation (which prior to the existence of dairy farming, meant breastfeeding a child until they were 5 or so) - such as the breasts getting larger, the mammary glands themselves getting bigger and getting ready to produce milk, and more fat being stored on the hips to ensure that the mother has sufficient energy reserves to support lactation. Additionally to be able to support pregnancy, her body produces more blood, so it's not just the baby growing blood, she's growing more blood for herself. Think of pregnancy as the baby plus the baby's life support system. The placenta isn't the only part of the life support system. And the changes in the breasts are also part of the baby's life support system, if you consider that breasts evolved to feed babies who are too small and weak to feed themselves. The mother's body essentially is the baby's entire life support system for 9 months inside and probably 7-9 months outside, and the baby would be dependent on milk alongside other foods for up to 5 years..... that's a huge toll on the mother's body, so that means a lot of changes within the body to be able to do that.

This idea of trying to gain as little weight as possible during pregnancy then shedding it as rapidly as possible after pregnancy isn't healthy. Women are supposed to gain weight during pregnancy, and some of it is supposed to be fat. Yes you can gain too much fat and that can be really bad too, but that doesn't mean that gaining no fat at all is optimal for health either. The rates of weight gains that midwives and obstetriticans use are a very good guide*, and yes, all that weight gain is necessary.

*they're based on averages, so there will be individual differences, where people gain different amounts of weight but if there are no health complications from it and the diet is full of healthy, nutritious foods and the mother isn't going hungry, it's all good

Losing fat slowly after breastfeeding is well established is safe and advisable, because that burns the extra fat stored to support lactation anyway (i.e. women are supposed to slowly lose the fat again while lactating, although some women don't lose easily while breastfeeding but lose it more easily after stopping breastfeeding). Lactation requires quite a bit more extra calories than pregnancy does, and how many calories you need during pregnancy varies according to what stage of pregnancy you're in. The body is capable of sustaining pregnancy and lactation on an inadequate diet, but that's not good for the mother or the baby, and while the mother will suffer nutritional deficiencies before the baby does, it can get to the point where the body will terminate the pregnancy, because it no longer has the resources to sustain it. During famines, rates of miscarriage go up drastically. And insufficient nutrition while lactating can result in the milk supply diminishing or in severe cases drying up altogether (which in evolutionary terms means the baby dying). But in most cases, the baby will be fine while the mother suffers nutritional deficiency disease as the body will take from its own reserves to give the nutrients to the baby.

Just adding 300 cals to your usual TDEE while pregnant is a bit simplistic, but it probably does average out to that over time. It's important to follow your body's signals though, if you're hungry all the time then you probably do need to eat more. Taking a prenatal vitamin supplement is a good idea especially in the 1st trimester and for 3 months beforehand, because the need for a whole range of micronutrients in that phase is very high. Iron is also very important, because you need to make a lot of blood, i.e. more of your own blood and the baby needs iron to grow blood too. Iron deficiency during pregnancy is very common as you really need a huge amount of it. Red meat and green vegetables are the best sources of it, and ensure adequate vitamin C to get better absorption of the iron. Calcium is vital when lactating, because that's when the baby's bones are becoming calcified and the baby needs a huge amount of calcium (which is why milk is high in calcium, but if you're not eating enough calcium, your body takes the calcium out of your own bones and puts it in the milk, and your bone density can be badly effected.)