You said you felt "addicted" a few min before the end of session.

She said "it's important to talk about addiction."

That sounds like standard therapy speak.

When you bring up a new idea just before the end of session, the therapist is trained to wrap up on time but tell you that they've heard you and assure that you can explore your idea next time. I don't think she specifically thinks addiction is a big deal for you or she'd have brought it up herself by now.

"Addiction" just seems like another way of expressing the discomfort that you have said you felt (and lots of us feel) about the primacy of the therapeutic relationship in your life and the longing for something it cannot deliver. That feeling is maybe heightened during an especially difficult time like grief or illness. I suspect your T means to validate you by using your word but is not implying anything more.

Remember Mister Rogers' closing theme song? "I'll be back when the week is new, and I'll have more ideas for you, you'll have things you'll want to talk about, I will too..."