Welcome to allnurses!
I'm not surprised the background check was thorough, and I wouldn't call contacting all your previous employers "invasive" -- it's actually pretty standard. It's an employer's market these days in most areas, and employers can afford to be as picky as they like. Plus, most employers have had bad experiences at some point with people they didn't
check out thoroughly. I have no idea whether that single incident will be a deal-breaker for your potential employer, but I hope this will work out for you.
I hope that at least some
of the people who post here, when people post and ask about leaving jobs they hate and whether they should or can quit without notice, "Sure! Do it! Life's too short! It's your life! Follow your dreams! Just don't use them as a reference in the future! You don't owe them anything!" (etc., etc., etc.) will see this. Getting flagged as "Do not rehire" by a previous employer matters. It's worth going to some trouble to avoid that. We boring old fogeys who keep telling people that it's important to always give the appropriate amount of notice, work your notice gracefully, and leave on good terms aren't just talking out of our hats.
As for your original questions, none of us knows what the employer will decide (of course, they are within their rights to decide to rescind the offer). At this point, there isn't really anything else you can do but wait to hear something back. You were correct to not badmouth the previous employer when you were asked about the situation. Going forward, you'll know to avoid having any more situations like that on your record, and, the more of a positive work history you build up over time, the less that one incident will matter.
Again, I hope that the job offer will work out for you. Best wishes!