A support ticket was also created in parallel with this post where we used the information that was provided here by our awesome support engineers to look a bit further on this matter. I wanted to update this post regarding the outcome of the case so those who may come across the same question could find an answer here.
The Data Source feature of the JVM tab is populated by the default metrics that are captured by the agent using an out-of-the-box solution. This requires using the supported technologies that @xlu linked in her response earlier. As you are using DBCP connection pool setting with Tomcat as web server the agent is not able to identify the default metrics that it looks for to populate the Data Source section. You can find the List of default metrics that the agent looks for Tomcat application here.
@jfalleur suggested the correct path to use custom instrumentation for these JMX metrics, but keep in mind that this approach tells the agent to capture these metrics but it will not be placed in the Datasource tab as this feature only gets populated by the default metrics. Based on our conversation here and also in the ticket, a workaround for this is to use the above to capture the metrics and then leverage Insights Metrics Exolorer to create dashboards for these metrics.
Adding DBCP connection pool setting with Tomcat as web server to the supported list of technologies for Data Source is a feature request at this point and we will proceed with creating a poll for this feature in the community as well.