To answer you quickly, yes it is possible via Request Attribute.
Thus, to have to do this properly, you have to select your Exception class name, please see below the screenshot :
Afterward, you will be able to plot onto your MDA chart as new detected placeholder, and eventually convert to custom metrics (calculated service metrics).
Yes indeed, need to do some customisation here.
Capture any request attributes using OneAgent SDK | Dynatrace news
Github link : https://github.com/Dynatrace/OneAgent-SDK-for-NodeJs#set-custom-request-attributes