How to connect the bath to electricity from home?
You need to put a separate circuit breaker to protect the line in the bathhouse in your switchboard, 25A will be enough, with such a cable section.
In the bathhouse, install another shield in which to install RCDs or difavtomaty. There is no specifics in your question, “how to do it right” depends on what you will feed in two whole phases in the bathhouse. I believe that it’s some kind of electric furnace, then you protect it with a separate difratom machine or a bunch of ordinary machines and RCDs. Lighting in the steam room is best done 12-volt. About the assembly of the electrical panel, we published an article, maybe it will be useful to you https://our.electricianexp.com/en/instrukciya-po-sborke-trexfaznogo-elektroshhita.html
You can equip a grounding conductor for re-grounding zero using a modular grounding kit - today it is the easiest option, and you will get a fairly reliable and high-quality result at the output. Such kits are produced and sold by many companies; I can’t single out individual manufacturers. Or do it the old fashioned way - driving 3 corners into the ground. In this case, the grounding will be the better, the larger the surface area of these corners and the deeper they are driven in. At home, you cannot fail to check the grounding resistance, so you cannot make a really high-quality ground electrode system. The only option is to make a deliberately redundant design, for example, to drive into the earth three as wide corners as possible or thick pipes of a meter by 2-2.5. But it is time consuming. It is better to turn to those who can make grounding that meets the requirements of regulatory documents.