@Rey Jhon :
Databricks-connect is used to run notebooks locally on your development environment, while remote clusters are used to run notebooks on a distributed cluster environment. In the context of the blog you linked, databricks-connect is used for unit testing notebooks locally, and the remote cluster is used to run the notebooks in a distributed environment.
If you want to see the job runs on the remote cluster, you need to deploy the notebooks to the remote cluster using one of the available deployment methods such as the Databricks CLI or the Databricks API. Once the notebooks are deployed, you can create and run jobs in Databricks to execute the deployed notebooks on the remote cluster.
In summary, you can use databricks-connect to test and develop notebooks locally, and then deploy them to the remote cluster to run them in a distributed environment and view the job runs.