In the U.S. at least there are several labs that print digital files using traditional-type silver-halide B&W papers and chemicals. I have attached a chart that I recently compiled on the ones I could readily identify. Some print on fiber-based paper, some print on resin-coated paper, and some print on both types. The available papers and surfaces differ, although most (all?) of the labs that offer prints on resin-coated paper use Ilford's paper designed to be printed on wet minilab-type equipment. Ilford sells that paper in glossy and 'pearl' surfaces. The pearl is about like luster. Personally I would have preferred Ilford to offer their 'satin' RC surface, which IMO is closer to matte. The range of prices is large, the cost of an 8x10 inch print running from $3.52 to $45.00 or more (toning etc.).
I have made some comparisons of RC prints from the first three (Mpix, Harman / Ilford, and Fromex / True B&W) with prints of the same files I made on a Canon Pro-100 (dye-ink) printer with papers with similar surfaces. Overall they are pretty close, but I won't say identical. Obviously if you are using pigment inks and/or matte papers the difference could be large.
What I cannot do is make close comparisons of these digital B&W prints to wet B&W prints from film. Not only have I not had a functioning wet darkroom since 2005, but there are too many process differences. I will let you experts discuss and debate that.
To me, potentially-important but unanswered questions include:
(1) are there any traditional-type B&W papers for sale today that are neutral (not warm-tone) that don't contain substantial amounts of OBAs?
(2) Does exposing the paper for a comparatively short time, to comparatively much more intense light, as is done with a typical digital printer, produce some effect that makes the resulting print differ substantially from one made under an enlarger with, say, a 10 s exposure? As a corollary, does the performance of papers designed for short, intense exposures differ meaningfully from the performance of papers designed for longer, less-intense exposures?