RQM REST/OSLC API to fetch the count of test artifacts in RQM 6.0.6
One answer
You could use OSLC query against a query capability for the project area of interest, and then count the number of resources returned in the results container. You can find more information about using OSLC Query at https://docs.oasis-open-projects.org/oslc-op/query/v3.0/ps01/oslc-query.html.
You can discover OSLC query capabilities from the OSLC Service Provider Catalog (see https://docs.oasis-open-projects.org/oslc-op/core/v3.0/ps01/discovery.html).
ETM seems to provide a separate query capability for each type of resource, for example, Test Suite, Test Plan, etc. So you would need to repeat that query for each of the artifact types that you were interested in.