Can You Use Classic Data Monitoring Tools for Model Monitoring?

You do not, at least for a variety of tasks, you do not really need specialized tools. Classic stacks such as primitizing, Grafana, CloudWatching, data dog can monitor a lot of important aspects of your model. But it doesn't mean that it's always the best thing to do because it does require you to build things that potentially you could get out of the box using an open source library or third party vendor.