@JohnRognes @JohnRognes thanks, yes, I had meanwhile collected this and a couple of other references and variants here: ncatlab.org/nlab/show/…

I should say that after realizing that the chat room here has been abandoned, I had taken the question to Charles Rezk's AlgTop forum here: faculty.math.illinois.edu/~rezk/discord.html

Unfortunately, I don't know how to search the discussion there to recover where exactly the exchange took place.

(It's weird that in 2021 there should not be decent forum software for scientific exchange. That "discord" server which Charles is using is aimed at gamers, of all people. Back in the old days, before "social media" was a term, there used to be USENET discussion fora which had no support for emoticons or memes or related nonsense, but did work rather well for actual discussion.)