One could simply say that a successful Sprint is one that has met its goal :
The Sprint Goal is an objective set for the Sprint that can be met through the implementation of Product Backlog. It
provides guidance to the Development Team on why it is building the
Increment. It is created during the Sprint Planning meeting. The
Sprint Goal gives the Development Team some flexibility regarding the
functionality implemented within the Sprint. The selected Product
Backlog items deliver one coherent function, which can be the Sprint
Goal. The Sprint Goal can be any other coherence that causes the
Development Team to work together rather than on separate initiatives.
(From the Scrum Guide)
The Sprint Goal is a first level of guidance for the Product Owner and development team. But based on that goal, the Scrum team could also perfectly agree on more detailed success criteria for the coming sprint. Typical (usually implicit) ones include completing all the stories, making all acceptance tests pass, but there could also be more exogenous indicators : customer satisfaction rate after a demo, budget obtained, CEO adhesion, performance minimums reached, etc.
As others have said, I think the answer to your question is : there are no predefined universal sprint success metrics. Success criteria primarily depend on strategic business goals of the moment and should preferably be agreed upon before the sprint starts, through the definition of a Sprint Goal and/or more precise sub-objectives.