I am looking for a way to control the processes from the Camunda engine without using the cockpit or REST API.There should probably be a dependency jar file for this.
The process logic is written in the BPMN file, but the control of the processes should be done neither through Cockpit nor through REST API. For example, decisions can be made through Java code, or arguments can be entered into methods related to processes, and this work can be implemented through the JAR file related to the Camunda engine.
If you don't want to use the REST API and are working with a Camunda 7 embedded engine approach, then the (only) answer is the Java API.
The different APIs are explained here: https://docs.camunda.org/manual/7.15/user-guide/process-engine/process-engine-api/
To start a process instance look at the RuntimeService. To get or complete tasks look at the TaskService.