That Joomla is throwing that message is not something I can fix from Modules Anywhere. That's down to how Joomla 4 & 5 work, depending on when the module gets loaded (and tries to load scripts and styles).
So where are you placing the {module} tag? In another module? In a component? In an article? And directly? Or is it included via other plugins?
I see on the internet that you are aware of this issue.
Then you should also have found my replies and solutions about this.