There's a lot of things you need to understand before attempting this type of fast and there's a lot of misinformation regarding the type of weight you actually lose during a fast like this. I read posts about this all the time and people think it's as simple as "hurdurrr your body burns fat before muscle I'm a doctor too hurhurrr"
If you're dealing with depression, you should consider talking to a doctor before you take an extreme diet task that can lead to substantial health problems or even eating disorders.
The first common misconception is that water fasting burns only fat. While yes you will lose fat, the truth a lot of people don't actually understand is you're also losing muscle mass which accounts for a large portion of the weight. Your muscle cells become damaged EVERY DAY from NORMAL use. Every day, all day. YES EVEN WITHOUT STRENGTH TRAINING. Muscle cells require PROTIEN to repair every night. Your body can't burn fat to repair your muscle cells. If they don't have protein, they will not be repaired. Now imagine all the muscle cells damaged every day through zero protein intake. That's going to be a TON of weight. MUSCLE WEIGHS SIGNIFICANTLY MORE THAN FAT. Yes you might like the way the scale talks to you after it, but you'll find that most people that do water fasts keep doing them to lose weight, because they're not actually losing as much fat as they think, and they really don't know what healthy habits are. These people continuously spread misinformation and know little about health.
There are ANIMAL studies that show slight benefits to water fasting but it is not deeply studied in people. Humans require many vitamins and minerals for body functions. There are some signs of permanent digestive system damage from going long instances of extreme fasting or starvation.
If you want to diet in a healthy way, try intermittent fasting at most. Eat good balanced meals, take a multivitamin, drink A LOT of water, consider taking some fiber supplements and load up on fruits and veggies. Focus on your BODY and health, not your weight.
Exercise can also help with your depression. Do some cardio, go for a walk outside. You don't have to bust your ass, just walk.
But seriously consider talking to a doctor, ask about helping your weight loss and take some professional advice. Good luck!