I think not discussing other relationships with therapists or being careful with wording so a new T doesn't get scared is the wrong way to go. If it were me, I'd rather figure out early that a T is uncomfortable with me getting attached and wanting to discuss our relationship at lengths. The way I act with my T is similar to how I do with other people. Though with my T, it's far more pronounced than with other people and he definitely gets a far worse version of me than most others. Sometimes he has to listen to things that are almost certainly uncomfortable for him, for example I'm pretty sure he'd rather not discuss his own death for an hour. But to me it's something important and I need to be able to talk through such things. If a T can't handle that, it wouldn't be the right T for me.

Similarly with this new guy. Either you censor yourself for all of your sessions, in that case I'd see it as a waste of money. In addition, it'd probably not work, at some point there's gonna be something about the relationship that needs discussing, unless you do something like pure CBT maybe. Or you are up front about having had some issues with other Ts. That way a new guy isn't surprised when it happens and you can tell whether working through such problems would even be an option.