The only major health risk is refeeding syndrome, and even then it's only really notable if you're an alcoholic or have anorexia. If you're otherwise healthy with normal sodium/potassium/etc. intake and you take it slow when refeeding, I don't think it's particularly dangerous. Obviously, talk to your doctor, and it's probably good to get blood work before doing something like this.

There's just not a metabolic pathway for breaking down muscle/organ tissue for energy when you have adequate fat stores. We would have died off as a species a long time ago if that were the case.

In the grand scheme of things, if you have the body fat, 7 days is nothing for a fast.

Edit: To those asking, yes. I fasted for 60 days, water and electrolytes, no calories.

Humans have weathered long durations of food insecurity for much of their existence. If the default metabolic solution to fasting was harvesting energy from skeletal muscle and smooth muscle... well that strategy wouldn't work for very long, would it? The lowest hanging fruit is muscle/liver glycogen, and fat mass after that.

Breaking down proteins (gluconeogenesis) is a metabolically expensive process, requiring large energy input for low energy output. The body is wholly invested in protecting these vital organs. Skeletal muscle has a reputation for being fickle, subject to change based on stimulus and energy demands, but those adjustments are most significant and relevant to those who are invested in maximizing lean mass (athletes, bodybuilders, statistical outliers).

Fasting is relatively protein-sparing, all things considered. The observations of apparent muscle loss can be attributed to loss of muscle turgidity - a reduction in glycogen, intracellular fluid, and electrolytes. The difference between fed and fasted states, both visual and internal perceptions, are quite extreme.

Are extended fasts ideal, or even generally recommended, for someone with the singular goal of building muscle? Absolutely not. But it is a flexible tool when goals shift towards catabolic outcomes (losing weight). Furthermore, the downstream benefits of fasting can translate to improvements in insulin sensitivity, nutrient partitioning, muscle-building, and body composition... which are relevant to anabolic outcomes.

"A 27-year-old male patient fasted under supervision for 382 days and has subsequently maintained his normal weight."

By comparison 7 days is trivial. More to the point, a 7 day fast with medical supervision should be safe, if it is not, the supervisor will advise against it.