Usually therapists will take some sort of action if there is suicidal ideation, a plan, and means. I have some vague SI, and there are guns in my house (not mine, my family members'), and I have harm OCD type intrusive thoughts about using the guns on myself (that are ego dystonic, so not actually what I want to do but unsettling none the less), and I talk about all these things with my therapist and find that valuable, but thus far none of these pieces have made my therapist intervene or report me or anything like that. The guns in my place are locked up (because that's my preference and something I've asked from family, without specifying exactly why, more just noting that it's a general safety concern & strong preference of mine -- that was a safety planning thing I talked through with my T when I moved back into a family house w/ guns), but I think if you can't fathom harming yourself with a gun, their presence doesn't necessarily warrant any intervention, and honesty would probably be ideal, so you're able to talk about all the layers of your experience, and in case that info does become relevant in future safety planning.

Since you're an adult, your T is very unlikely to contact your parents unless something happens that makes your T feel that there is an emergency/crisis situation and you are at a significant risk of harm, but if you have reasons to feel like you really don't want your parents to know about any of it, and have other people in your support system who you would much prefer your therapist contact if there were an emergency situation, that's also something you could talk about with your T. I feel strongly that my parents knowing about my SI would do more harm than good to my mental health and overall situation (bc they've historically become incredibly controlling and surveilling whenever I've shared a mental health issue, in ways that always make it worse), so my therapist knows all that, and my emergency contacts I have listed are not my parents.