I‘m hoping a pro will weight in. But probably you’ll need to do some selective demo to determine what is going on the the wall and near the curb. You can do that yourself (carefully) or hire a tole pro to come look at it. Tile pros are experts in waterproofing, not just tile. They can probably diagnose this for you, and tell you what action is needed.

Here are some resources you can use to find a tile pro:

www.tile-assn.com

www.ceramictilefoundation.org

www.ceramictilefoundation.org/find-certified-tile-installers

www.tcnatile.com/products-and-services/publications.html

Classic water damage from leaking. That vintage shower more than likely has zero waterproofing.

Seems like more extensive damage than just the occasional spatter of water and low ventilation. From these photos I wouldn't be surprised if your walls are quite damp all the way up, likely older drywall that's been soaking up water for some years now, possibly because of inadequate waterproofing in the shower construction. Repainting won't help; new paint won't stick.

You will probably need to carefully remove one of those walls to check the situation beneath.