This looks less like an issue with Insert Dynamic Text itself and more like a problem with the rich text editor (CKEditor) introduced or updated in 9.1.45.11.
Based on the console errors you've shared:
HTTP 500 when requesting msdyn_customcontrolextendedsettings suggests the server is failing to return the configuration for the rich text control.
CKEditor: editor-plugin-required indicates one or more required CKEditor plugins (for example, toolbar/clipboard) are not loading correctly.
The subsequent JavaScript errors (formContext.getControl is not a function, clearFormNotification) are likely cascading failures after the editor fails to initialize.
A few things I'd check:
Verify that all solution components related to the Rich Text Editor control were updated successfully during the upgrade and that no web resources are missing.
Review the IIS and Dynamics server event logs for the corresponding 500 error to identify the server-side exception.
Test whether the issue occurs in an out-of-the-box Email Template with all custom JavaScript disabled. This helps determine whether it's a product regression or a customization conflict.
Clear browser cache and ensure the latest web resources are being served (or test in an InPrivate session).
Compare the upgraded environment with another environment (if available) running the same build to see whether msdyn_customcontrolextendedsettings returns successfully.
Since the issue started immediately after upgrading to 9.1.45.11 and the feature worked before, I'd also recommend checking whether this build introduced a known regression with the UCI Rich Text Editor. If the behavior is reproducible in an uncustomized environment, I'd strongly suggest opening a Microsoft Support case, as the combination of the 500 response and CKEditor plugin initialization failure points toward a platform issue rather than a configuration issue.
Out of curiosity:
Does this occur for all Email Templates or only specific ones?
Have you tested in a completely clean organization with no custom JavaScript or custom controls?
Are there any reverse proxies, load balancers, or IIS URL Rewrite rules that could be affecting requests to the CKEditor resources?