This is a bunch of pseudoscience.

"Starvation mode" as people talk about it is generally nonsense - the exceedingly low bodyfat you mention for keto is the same place you would see it in a non-keto diet when we talk about actual starvation mode and not whatever you're talking about with a non-ketogenic diet.

The only real difference when it comes to the biology here is that fat mobilization into glucose is significantly slower and less efficient, which keeps your blood sugar levels more constant, which results in fewer post-meal food cravings. Which isn't nothing, but it's not muscle sparing in and of itself.

We have plenty of studies here. Keto diets are not better for sparing lbm.

https://pubmed.ncbi.nlm.nih.gov/38934469/

In fact, if you already have significant muscle mass, it might be worse. Glycogen is hugely important when doing resistance training, and keto significantly impacts your glycogen stores. People perform worse with their resistance training on keto than regular diets.

https://pmc.ncbi.nlm.nih.gov/articles/PMC9244428/ https://pmc.ncbi.nlm.nih.gov/articles/PMC8469041/