Answer
This is a confirmed, documented platform limitation — Assistants currently don't support Custom Attributes at all, so a custom attribute simply won't be available (or won't reliably persist) on any Assistant-driven page, regardless of how it's added to the underlying entity or worked around with a group; check IFS's documented known-limitations list for the current status of this gap rather than continuing to adjust the custom attribute or page layout to try to make it work.