I'm a big pragmatist. Here's a big part of my strategy... .at least since I've learned about the BPD circus!
Don't say things because they are true.
Say them because they will make life better for you, and possibly your husband as well. (While not being actively deceitful or lying if you can avoid it.)
Before you open your mouth to say something (or include it in a note), ask yourself: "What good will come of saying this?"
I guarantee that you won't be getting any validation for your feelings or your reasons for going away from your husband. You will get dysregulation and blaming, etc. instead. Seek that validation elsewhere. [Here... .your sister... .your therapist, etc.]
Getting out of the house tomorrow protects you. You just need to do it, and should tell your H that you did it. He has had plenty of warning anyhow. Don't bite on temporary, permanent, or whatever.
If leaving him the car works for you, do it. Say as little as possible about it.
If your lawyer says he can't take you off his whether he wants to or not, just shut up about it.
The time to offer to pay half will come later... .after he figures this out. You can offer to do it retroactively when you do, if you are still feeling generous.
It is probably easier to leave a note than talk to him... .but keep it short. Something like:
I need to live apart from you right now.
I know this is hard for you and I'm sorry about that.
You can drive the car for now.
(Optionally say something about where you are staying or how he can contact you.)
Say goodbye to the neighborhood. Or perhaps "So Long." You certainly can go back to visit if you want. You will be looking for a place to live in a few months, other than your sister's basement. Lots of possibilities are going to exist for you.
Focus on finding your own peace with existing on your own. (You said that leaving a r/s without another one already lined up to jump into is a huge step forward for you!) After you work through some of your triggers, you will be able to imagine what reconciliation might look like. Accept the uncertainty. It is hard. (And even harder for a pwBPD like your H)
You will give him room to deal with his own issues... .as well or as badly as he's going to.