I've told my therapist about my suicidal ideations, including vague plans. I discussed such things perhaps... three times during the ugliest phase of my trauma work. The reaction varied depending on the situation.

Once she didn't really comment much that I recall as I think I did not sound serious.
Once she asked me if I had an intention to kill myself. I answered, honestly, no, I didn't.
Once she actually told me "I need you to stop talking like that" - that was her way of warning me that she would need to escalate the situation if I could not rein myself in and I think trying to get me to be more productive/connected to her, not get lost down that path. I gathered myself back up and became 5% more reasonable.

I found the suicidal ideations comforting, but more as a fantasy, though sometimes a tempting one, than something I could carry out.