You might not be able to achieve this via OOTB apis however, there are few ways to achieve this
You could create a custom workflow that accepts the manager name (and/or workitem name) and returns the number of pending workitems for the same.
Abd then utilise the OOTB SCIM api to launch a workflow.
Create a REST plugin that provides an endpoint and based on the input (manager name and/or workgroup), fetches the pending workitem and returns it in a json format.
Please keep in mind to make sure that you add authorization on top of the rest endpoints via capabilities and sprights so that only allowed identities can call the endpoint.
There you go communityrestapi.1.0.zip (77.4 KB)
you have to grant to the proxy user communityRoleRESTAllow sp_right and than you can use postman to count approvals,