I'm from Australia but I can say I've been fairly forward about method and desire to CTB with previous mental health professionals. It probably varies between professions if I had to guess from my experiences. The pattern I've noticed is unless they genuinely think that you are in immediate harm of killing yourself or harming someone, they won't do anything. Probably depends on the person, whether they have lived-experience, just the overall context of you, etc.
i'm in canada, the us might have similar rules. im guessing i cant mention that i think about suicide :/
I'm 99% sure you'd be able to say that you
think about suicide and not get hospitalised for that. If you're saying that you
want to kill yourself, then it might be a bit different. If you start saying how you want to die, when you will, giving very concrete and actionable details, then they might get a bit more concerned.
Generally you'd be better off being honest with how you're doing if they are a good therapist.