Sorry, but this doesn't make sense to me. B&W is an image that has only black, white, and shades of gray. This certainly exists with digital. I have a big, digital B&W print hanging a few meters from me.
I think you are mixing three things:
First, a "B&W" conversion may actually be monochrome. However, others aren't. For example, the LR B&W profile does not add color, AFAIK.
Second, the various "B&W" conversions differ in how they treat the three color channels. This is true of both monochrome and true B&W conversions. In effect, they are doing what one does with color filters in shooting B&W film. I don't use film emulations, but I think that is part of what they do as well.
Third, papers add another element to this--essentially, adding color cast to even perfectly B&W images. Back in the Pleistocene era when I shot only B&W film, most people I knew were using Kodak papers. I disliked their warm tone and instead usually used Agfa Brovira, which was a very cold white. The same is true now. When I print B&W, I have to choose the tone of the paper I use, and some are colder white than others. For example, one paper I use (no longer produced) is Breathing Color River Stone Satin Rag. It's a zero-OBA paper and is visibly warmer than something like Canson Baryta Photographique. That is, it adds a very small bit of color in the yellow-brown range. Does that mean that a purely B&W image printed on that paper is now monochrome, not B&W? If you answer yes, than all of my old friends who shot Tri-X and Plus-X and printed on Kodak paper were making monochrome images, not B&W.
Digital cameras don't record color. They only record data that is mapped to color by software. Somewhere, early on, some software engineer decided that a saturation value of zero maps to "this" and called it B&W. It appears to have become the default in the digital world. To my eye, "this" runs a little warm. I got no problem fixing that and I'm still going to call it B&W, even if it doesn't exactly, mathematically, match an arbitrary saturation zero.
(Have you ever tried to recover blown highlights in post from a color file? With no color data, you get that nasty, muddy, ugly, saturation-zero density. That's mathematically B&W.)
During the Pleistocene I used a lot of different photo papers, but I bought my Ilford Cold Tone by the 500-sheet box and it never occurred to me that I was making anything but B&W prints. I have several that I made during that era hanging a few meters from me. All B&W. All developed in Dektol, same as all the other B&W paper I used. No special handling required.
I worked at newspapers, and while I got to order my own supplies, the photo paper didn't matter at all. My photo prints were turned into halftones, then put on newsprint with black ink that each had their own tone. Other than a preference for glossy, the folks making the halftones didn't care at all about which photo paper it was on or whether it was really B&W. That question never came up. My preference for photo paper was entirely personal, and since nobody cared, I got cold tone. The price was the same, it handled the same, it was just another B&W paper in the cooler at the camera store.
Do all photo software packages produce the same tone for saturation zero? I'm not sure how we'd test that. Too much discrete hardware and software exists between the exposure and the presentation.
Colored filters used with B&W film work at the wavelength level. If you want to darken up your skies, you throw on a yellow filter. Yellow blocks the blue wavelength. Skies are mostly blue, and no blue light gets past the yellow filter to the negative, hence, darker skies. Software can mimic that based on color data the camera collected. While the actual light waves involved are long gone, the data is easily changed.
"If you answer yes, than all of my old friends who shot Tri-X and Plus-X and printed on Kodak paper were making monochrome images, not B&W."
You mentioned a lot of different B&W photo paper brands and types. Which one was your saturation zero? Which one influenced that engineer? Ilford Cold Tone was my zero for B&W. Still is.