It appears this may be an issue with the module builder. The team is aware and is looking into it, thank you all for reporting your feedback with this issue!
In the meantime, here is a workaround that I've tested that can work until we hear back official word from the support team.
Mapping External Templates for Sitefinity 4 Widgets
If you look at Option 2, you can create a physical template file in the folder ~/SfCtrlPresentation
/ using the naming convention described and the Guid for the template from the Advanced settings of the dynamic module widget.
If you name everything correctly, the control will automatically pick up the external template file instead of the embedded one. just be sure to build your project if you are using a full user control (code behind).
I hope this is helpful, let me know if you encounter issues or have additional questions!