How to locate a specific slide using a certain layout in Google Slides?

I'm looking almost for the same, but not figured out how to find and list all layout names it the Master.

Probably you should use script to find specific layouts[] object for (Page)

The layouts in the presentation. A layout is a template that determines how content is arranged and styled on the slides that inherit from that layout. From https://developers.google.com/slides/reference/rest/v1/presentations?hl=en

See more about Pages, Page Elements, and Properties

There is some code sample for the layouts search:

// The following line opens my presentation
var presentation = SlidesApp.openById('PresentationID');
// this will return an array of all the layouts
var layouts = presentation.getLayouts();

//if your first array item is the office layout
var newSlide = presentation.appendSlide(layouts[0]);

//Orelse you can search for your layout
var selectedLayout;
for(var item in layouts)
{
   //Logger.log(layouts[item].getLayoutName());
   if(layouts[item].getLayoutName() =='CUSTOM_1')
   {
     selectedLayout = layouts[item];
   }
}