A quick google search seems to confirm that fasting can indeed help with depression:
https://link.springer.com/article/10.1007/s12603-013-0344-9
https://www.sciencedirect.com/science/article/pii/S027858462...
https://link.springer.com/article/10.1007/s12603-013-0344-9
https://www.sciencedirect.com/science/article/pii/S027858462...
I experienced none of the effects. People claim to be sharper and more energised during fast, but all I experienced was noticeable sluggishness (no glucose, only fat as energy source) and bit more pissy about small things (though I recognise it and never act on it).
P.S. Worth mentioning, any water fast above 4 days can be potentially dangerous if you don't take supplements that regulate your bodily functions, like salt, potassium, magnesium etc. I have read accounts of people doing only water fast no supplements for 10-15 days and report serious symptoms of their body shutting down (maily cells dying due to lack of salt).
Care must be taken to avoid potassium overdose if supplementing with potassium. Sodium chloride is well tolerated on the order of no more than 20 grams per day spread out over the whole day.