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Happy to answer your query.
Please allow me a moment to explain about triggers vs pipelines.
Triggers and pipelines are different. The main purpose of a trigger is to start / kick-off a pipeline run. In most cases what you want to track is the pipeline run status, not the trigger status.
For scheduled triggers and event triggers: If the trigger fails, the pipeline never starts. If the trigger succeeds, the pipeline run starts. The trigger does not care about whether the pipeline succeeds or fails, only that it starts.
Also, please note that a pipeline run can succeed even if one of its activities fails. That is a separate topic.
While rare, a trigger can fail. This could be due to concurrency, throttling, or something else.