I would have a chat to your T first about the kinds of things that they would need to report as therapists have different ideas. However, non-suicidal SI is normally not something that therapists will report.

Most therapists should understand that SI isnot an attempt at suicide or a real threat to your health, unless it becomes extreme. Most therapists will use it as an opportunity to start talking about the reasons you feel you need to SI and help work through those emotions.