Issue with "Hide if Empty" Module

We are having an issue with a Related Posts Module by EasyBlog
Joomla Version: 4.2.x
Advanced Module Manager Pro - Latest

We have created a Related Posts Module with the setting "Hide if empty" enabled (see hide-if-empty.png).
However, if we select a style for the module (see style-setting.png) this no longer works properly (see not-hiding.png). The module is only hidden if we keep the module style set to "None." Obviously this is not ideal, because we need to add styling to the module to be in line with the site's design and give visual separation from the rest of the content.

Please advise on how we can get the "hide if empty" working while a module style is set.

Given that this module is by EasyBlog, we reached out to them first. However, they insisted we reach out to you since the hide if empty functionality is not native to their module.

The styling would come from the YOOtheme template.
I don't think it's Easyblog's output causing the issue. The reason I believe this is because if we leave the template style to blank, the module hides properly if no tags are present (thus confirming easyblog is not outputting data when there are not tags).
However, as soon as we select a style, even if the easyblog output is blank, the module still loads blank.
Do you agree that this makes it sound like an issue with either the template or advanced module manager, not easyblog?
Does the above give you any more guidance in what the issue could be?

I'm not sure how we would change the ordering without negatively impacting the template though at this point.