I have been in that place where my depression didn't feel so much sad as "blah" and disappointed with life and stuck. I would think about suicide almost every day. I rarely thought about plans, though, so that part of what you said concerns me a little more. It sort of depends how detailed your thoughts about the plans are.
But anyway, I talked to my therapist about the suicidal thoughts and we talked about what these thoughts might be doing for me. It seemed that they were acting as a distraction from other thoughts that were causing me great anxiety.
If I started having thoughts that were really upsetting to me, I would say to myself "well, if things get really bad, I can always kill myself." And then I'd feel worried that I was thinking that and my thoughts would be off onto the subject of suicide and away from whatever was really bothering me.
I don't know if this is at all like what's going on with you. We can only offer our own experiences sometimes to see if they resonate with someone else.
After I had this discussion with my therapist, the thoughts of suicide went away completely for several weeks. Now I'm having the occasional thought about it.
My therapist always asks me to thank the part of me that's trying to help, even if it's doing it in a maladapted, ineffective way.

It's part of the IFS (Internal Family Systems) therapy model.
I do think you should bring this up with your therapist. If you are not seriously intending to carry out your plans, make that clear to them, but it could be really helpful to talk with them about why you might be having thoughts of suicide so often.
Your last question about people who never think about suicide - yes, there are people who never think about it. Or at least they haven't yet at that point in their lives.
I was in my late teens the first time the thought of suicide ever crossed my mind and it was highly alarming. I had a few thoughts about it then and then not again until my mid-20s. Since that time, the thoughts come and go and have come to seem fairly...well, not normal exactly, but familiar. I'd prefer not to have the thoughts, though.
You might like a book called "
Night Falls Fast: Understanding Suicide" by Kay Redfield Jamison. She is a professor of psychiatry at Johns Hopkins and is also bipolar. She is a good writer and combines statistics about suicide with stories of real people. It's a really good book and might help to answer your question about whether thoughts of suicide are always a sign of depression.