Although this isn't yet a strong answer, the following may be a point of interest, depending on what it exactly means.
We know there was huge campaign for: Justice for Barb and the Duffer Brothers did promise this would addressed.
As one of the previous answer's sites, season 2 does feature a subplot in which Nancy seeks to avenge Barb and does address the state of Barb's parents. However season two also does some other interesting things by giving viewers a decant and morally conscious scientist in Dr. Owens, and despite Brenner's missteps and abuses towards Eleven (and Eight), it once again reinforces that the scientist are only partially responsible for Barb's death, as it was Eleven whom accidentally blew open a hole to the other dimension and that the scientist themselves do not understand the nature of the Upside Down. This makes the actions of Nancy not necessarily better for Hawkins and it's residents, because we see Dr. Owens sincerely or genuinely trying to be helpful and be more honest about what they do and do not know. So in theory, should Dr. Brenner still be alive, the Hawkins Lab, now under investigation, may remove Owens and reinstate Brenner, seeing Owens as a bigger screw-up. (The reason this relevant is because it remains to be seen how Nancy's choices towards wanting 'Justice for Barb' effects everything, which may tell us, eventually, if this action really is justice or not--subjectively, speaking.)
The other interesting things the season may have done to touch on Barb might have to do with "B" alliteration. Two of the new characters, Billy and Bob both have "B" first names, with Bob being in parallel by being a somewhat geeky innocent character that didn't deserve to die from spawn of Demigorgon, and whose name is similar sounding to Barb's. Curiously Bob also tells Will about his dreams, being intimated by an antagonistic-figure, which he refers to as Mr. Boldo (again "B" alliteration).
In addition Nancy comes across a person that looks like Barb from the back, whose not Barb (possibly a 'Ghostbuster' allusion or pun -- and Nancy is also wearing "Barb" colors, as is the Not-Barb) and when Eleven goes and stays with Eight in the warehouse, there the name "Barbelith" graffitied on a wall, which is also a reference to Grant Morison's The Invisables comic. (I will come back with a screen cap, if I can find one).
Note: Scientist have to go into Upside Down to fix Upside Down version of a satiate to get there equipment to better work.
In The Invisibles, Barbelith is the name of the "placenta" for
humanity; a satellite-like object located on the dark side of the
moon. It recurs throughout the story as a supernatural moon seeming
both intelligent and benign. Barbelith's role is like that of a
placenta in that it connects the hologram of our subjective reality to
the realm outside of our space-time, the domain of the magic mirror,
and helps humans to realize their true nature beyond the subjective
concept of "self".
Grant Morrison describes its origins as follows: "The word 'BARBELiTH'
is derived from a dream I had when I was about 20 or 21 and coincided
with my first structured 'magical' experiences and a minor nervous
breakdown (in the dream, BARBELiTH was the name of some higher
dimension or alternate reality)."
So it's unclear what all of these things add up to. Whether it might be the Duffer Brothers trolling fans, paying homage to Barb by continuing to acknowledge her both in plot and in subtext, or if the Barbelith is pointing to some kind revenge story for a "mutated" monster-Barb (thinking it could also play on a Hell allegory to Lilith) or of Barb's consciousness is preserved in the Upside Down somehow????
Some additional info on the original intent of the character Bob, and the changes made, have come to light through interviews with The Duffer Brothers. I'm adding this on, because their reason for the change also includes the purpose of Bob, as it relates to Joyce, by siting that his death is a motivator for her to now avenge him--solidifying my suggestion that Joyce is then in parallel to Nancy, and thus Bob is in parallel to Barb.
“That was never on the table. We had talked about the death of some
major characters, that may or may not happen in the future near or
far. But that was never part of the discussion for Season 2. The death
of Bob was initially much earlier. In fact, in an early outline, Evil
Will kill him in like Episode 3.”
“We wanted to keep him alive longer, and then use his death as Joyce’s
engine,” Levy said. “The avenging of that would become Joyce’s engine
for the finale.”