I would ask your tile person about the treatment. Since marble requires regular resealing and treatment there may be some solution to your issue. Marble is a porous material.

Marble is loaded with minerals, these minerals react with the quality of youre water source, It is not uncommon in marbles to see rust tones become more prevalent with time. Likely from Iron content.

If you are only seeing this on exterior walls share some pictures ....Does the discoloring happen to align with your shower heads and/or areas that see the most water immersion?

So much can go wrong with steam showers from every single decision made in the build and marble is the last and least wise decision in regards to longevity and maintenance.

If it is not simply minerals oxidizing/bleeding?

One of the first questions I would ask is if your Thinset Cured completely and that it is rated for submersible applications.( requiring a minimum of 30+ days depending on site conditions, and that your grout also reached a full cure prior to sealing and re-introducing water and worse Steam. Many thinsets have additives/ that are not specified for steamers and Can leach latex and the like.

sorry to hear of your misfortune, maybe, hopefully its just Nature at work?

Stop using it for a few weeks and put a dehumidifier inside the shower , let it dry and see what happens....

How difficult to care for the marble slab in shower?I'm about to install a surround for my tub area.terrufied as I'm not very clean.used quartz in kitchen

But my niece tries to get me to use natural as never gets outdated