Quick update – According to another support request, the shortcode only works when the member is logged in, it throws a script error otherwise. Once I removed the button from the pages that had access without login, the problem went away.
Two takeaways/recommendations for the devs:
1. The written documentation needs updating. There is no info about the shortcode, nor is there any info about potential issues with non-logged-in members.
2. It seems to me that a simple check-script would likely solve the broken code/script issue when on a more open placement is used.
Feature request? Maybe allow size/color changes for the button? Or at least use the discord colors – your lime green is very… bright, verging on garish.
TLDR – problem worked around until the next update, hopefully.