Thanks Vicente for the quick reply.
I did a bit more digging and I think I understand what’s happening.
The Paperpile extension was failing to load at all on both scholar.google.com and google.com. Two symptoms: (1) the pop-up button was showing the “Waiting for page to load…” message even after the page was fully loaded, and (2) the extension background page showed an error message “This page cannot be scripted due to an ExtensionsSettings policy”.
Reading up on that message, it seems this is a restriction that can be applied to managed Chrome browsers (Configure ExtensionSettings policy - Google Chrome Enterprise Help).
I had been trying on my work-managed laptop. Switching to a different machine w/ the same non-work Chrome account, Scholar buttons showed up fine.
I wonder if @Miki_Katsuragi was encountering the same issue.