These days Rest API using Spring Boot can be easily developed along with frontends in Vue or React or Angular to define business workflows in a small service business for example a company that sells life insurance. In this business there are workflows like employee login and adding a new prospective customer to Customer database, workflows like sending emails to prospective customers when new life insurance product is launched meeting the customer requirements etc. Another employee with different role when logins see directory of employees or add new employee or delete employee workflows. Half of these workflows already implemented without using BPMN.
Given above why I as developer need BPMN 2.0 and in particular Activiti (link here) ? BPMN is very complex spec and learning this spec and Activiti is extremely time consuming.
I cannot understand how embedding activiti engine jar in my existing project and design BPMN 2.0 workflows would make my business run more efficiently.
You need to find the right balance and the right tool for the right job. The BPMN spec was created by different industries that wanted to standardise how the work gets done in large companies and governments. Some of the advantages of using something like Activiti becomes really apparent when the job that is being done is too difficult to monitor (or event understand) without business process definitions.
If you have one small service for a small company, probably it is too much. Notice that Business Processes usually help a lot in places where the companies/orgs have big problems in sharing how the work gets done and by whom. In such situations, understanding how many business processes are executed and which ones are getting stuck (or where the bottleneck are) is really important (cost and resources saving and improved efficiency).
You can leverage frameworks like Activiti, by starting with a small business process, and then adding more and more business definitions to help your company to understand how the work is being done and also to measure and compare with previous months or years. You can compare trends and then improve your business processes, hire more people in key areas or redefine completely how the business is being run.
Hope this helps.