The black and white photos taken by those photographers are all in black and white mode? Or late PS?

If it's film, it must be black and white film itself.

It is black and white.

If the photographer uses a digital camera and uses the raw format, it doesn't matter whether it is black and white, because raw is the original document and contains all colors. Even if it was taken in black and white, the final result was a document with all colors. You can choose black and white or color later.

If you use a digital camera and jpg format, photographers usually choose color to shoot, because they can ps in black and white when they go back. If sometimes they find that some films are more suitable in color, but they use black and white, but they can't restore the color.

There is also a photographer who only shoots in black and white and never shoots in color. Of course, there is no need to shoot in color. Of course, this is only a minority.