I'm so sorry for your loss.
This is not my story, but it could have been. I have a long time on-again-off-again partner, Davis, who has struggled with depression, who has been suicidal at times, and who has had difficulties with poly.
It is not your fault. It was B's responsibility to get himself the help he needed. If he really felt that he was on the brink, he should have been calling 911, not you. It was not fair of him to put that on you. I'm sure that he was indeed an amazing, one of a kind person -- isn't everyone we love? -- but he acted selfishly in leaving you in this way, in such a way that it would be practically unavoidable for you to feel an immense amount of guilt along with your grief.
I hope with all of my heart that Davis will never decide that he has to leave this world prematurely. He FINALLY started therapy recently, so hopefully the chances of that will be less. But if he does ever find it all to be too much, I genuinely believe that his love for me is such that he will do what he can to mitigate any responsibility I might feel, via a note at least, because he wouldn't want me to carry that forever.
B wasn't thinking clearly, of course, so he can be cut at least a tiny bit of slack for leaving you in this position. But that still doesn't make it in any way your fault. You say he suffered from deep depression, anxiety, and alcoholism. Any one of those problems can be more than a partner can possibly help with, and all three in combination are practically guaranteed to be overwhelming.
You are not a health care professional, much less the suite of them that it sounds like he needed. Even if you'd come home and managed to help him this time, what about the next time he felt so low, or the next, or the next? He needed a level of care and intervention that was beyond what you could possibly provide, and, again, that was HIS responsibility to pursue. It was his responsibility because mental health HAS to be our own responsibility, for the simple fact that we CAN'T get better unless we ourselves choose to fight for it.
I wish you the best. It wasn't your fault. Other people who don't understand poly won't understand, and that's unfortunate, but it doesn't change the fact that it wasn't your fault. Even if you were cheating on him -- which you were not! -- suicide was still his own choice and not your fault.
It was incredibly shitty and unethical of that office worker to divulge personal information about you, and they should be reported and fired before they violate someone else's privacy! What am awful position that's put you in, in regards to getting your own care! I hope that you can find a place unconnected to your ex, where you can get help. Best of luck.