Most mid-war barrels will have a date, code that identifies the provider of the raw forging (steel mill), the lot number and the finisher will be identified either by waffenamt (if in-house) or if a sub-contractor by an ordnance code.
Early on this is often hidden under the stock, but by 1940 or so they increasingly are seen above the wood line. S&S (Sauer) and Gustloff Weimar are notorious for having at least a partial above the wood line.
Both used key sub-contractors extensively, S&S often used other nearby firms (BSW, CGH etc..); Gustloff Weimar used just about every barrel finisher that outsourced.
Most often Gustloff used Ruhrstahl, as they were part of the Saxony Group organized for the purpose of providing Gustloff with parts to assemble (Gustloff was designed to be an assembler from the beginning, using smaller specialized firms that made components).
Perhaps the most intriguing firm we follow is Gustloff Weimar, as they offer the most variation. You can find elusive guo barrels (AI in the Netherlands), FN made barrels, or even the occasional bcd made barrels later in the war (43-44).
Anyway, knowing the BC will not add value to your rifle usually, however it can add to our understanding of how the rifles were made, the interactions between firms, and it often encourages collectors to contribute to your thread.
I know I find it much less tedious to post if I get a BC, or some “data-poaching” for my research.