To run the process, you have to first release and then deploy the business process project.
Releasing a project creates a version or snapshot of the changes, and deploying the project makes it available in runtime to be consumed. You can only deploy a released version of the project.
In the Process Builder, to release a project, ChooseRelease button on the top-right corner of the screen and provide a description in the popup dialog.

Every time you release, a new version will be created. The version is incremented automatically based on how you want to store the changes in the repository like major or minor update or just as a patch.
If you are releasing for the first time, then the version will start with 1.0.0. Next time you release, the version numbers will be automatically updated.
Choose the Release button.

Once the project is released successfully, choose the Deploy button on the top-right corner of the screen.

Note: If you do not see the Deploy option you may ned to manually change from the Editable to the Released version of your project:

Select the Public environment and Choose Deploy.

Choose Deploy.

Select the destination S4HANA_CLOUD_CPI from the drop down and Choose Deploy.

Once the deployment is successful, you will see a changed status.

You cannot edit released or deployed projects. To continue working on your project, you need to select the Editable version of your project (at the top of the page).
After you have released and deployed the process, go to the SAP Build Lobby and find your project (i.e. Sales Orders Management ).
Once you have found the process with at least one available version, Choose the Navigate arrow on the right.

Select the Versions tab, locate your Deployed version, and select the Publish to Library icon.

Select the version (you may use the most recent version - if several versions are available) and choose the Publish button. Afterwards, your process is ready to run.

You have successfully released, deployed, and published your process. Now, your process will be visible from other SAP Build products in the SAP Build Library section. It is time to test the process and see the results.