I’m not fully familiar with the packaging processes for Steam but did you double check that the “Include Prerequisites” box is checked in your packaging settings? If you are building from source, it might be worth checking out BootstrapPackagedGame.cpp. It is a cool processes that kicks off the prereq install work you are interested in. The dependency checks performed before the prereq installer is kicked off could be problematic. The checks do not seem robust enough to catch all the missing dependency edge cases. I’ll try to bring it up with the source author.
For some reason I’m not able to follow the link you posted to your answerhub question but I think I have an idea what you are asking there from the URL. The answer is a bit complicated because the installer takes into account a large number of windows versions which have their own little requirements. See my reply to PrimalJohn Scott to see the general list of items installed. We can go into more detail on each one as needed.