Ok, found the problem.
It is fixed on your setup and in the latest development release of ReReplacer on:
regularlabs.com/development-releases

The ReReplacer item should be set to Search Area 'Component'.
Anything replaced after that is at a stage where you can no longer add style/scripts to the document.
Joomla 4 has chosen to break bad when something tries anyway.

The reason ReReplacer needs to be ordered before Modules Anywhere is for above reason.

If Modules Anywhere is set before ReReplacer, then ReReplacer will place the {module} tag at the correct stage (onAfterDispatch), but Modules Anywhere will not see it at that stage (as it was ordered before and already took its turn).
So it will then try to replace the {module} tag at a stage in the rendering process (onAfterRender) where Joomla has already locked the assets manager.