Yes, I thought it may be to do with graphic rendering. I checked my second system, which was not up-to-date. Updating Heidi to the latest, all is well with the pop-up working. The Wine version is close at v8.18. Letting the desktop system update which applies a major update to KDE Plasma breaks it.
I think you can mark this issue as resolved, though the pop-up itself must make a unique call to the system to display. Are there specific parameters passed which are not handled and result in the blank pop-up? I can work with this feature turned off for now. Heidi remains my preferred DB tool for MySQL work!