You want to see a process tab for an Idea or Project in the Modern UX so that end-users can run any process manually.
Release : 16+
You can complete this by creating a new Blueprint for Idea or Project only if the process is associated with the object. If the process is not associated with an object, it will not be available to add.
You will see the process on the top left. If there are multiple processes added, you will see an Actions drop down.