You can't pause only a project as plans are billed by workspace.

However, to stop your deployments and minimize costs, you can:

Go to your services, click on the options of the active deployment, and remove it. This will not delete the service.

Then, go to your Workspace settings > billing and cancel your plan. This will automatically downgrade you to the Free plan.

Keep in mind that you will still be billed for storage costs, even on the Free plan.