"[...] the deep shit. Like that shoulder to cry on, person to call when I'm excited, or vent to, or overall bullshit with. [...] I feel like connections like that can only develop over time and through vulnerability and fostering intimate settings to be such. I'm asking for someone who is willing to get there together. "
So basically, you want a relationship. What you don't want, is an abusive relationship, which for the time being I'll assume is what happened. This isn't coming from a bad intention or meant to insult you or anything, just an observation of a contradiction I see in a lot of people's lives that most likely (but not 100%) applies to you too.
People will spout out niceguys at me, but if you're one of those women in an abusive relationship, that's not a relationship. If he humiliates or abuses you or mistreats you a lot, maybe even a little, that's not a relationship. There are plenty of men, who yes, have issues. Social, financial, mental, whatever else, etc.
But they'd never abuse you like that. It's just taboo that men complain about the jerks getting the girl, because people think they're entitled to relationships. No one is entitled to a relationship, it's just that women keep ending up with the physically/emotionally abusive jerks instead as if it's a better choice than a boring/awkward/whatever guy. I see this all the time. Just go to the dating or relationship subreddits, it's full of it.
I see a lot of people with divorced parents or single parents, and I'm lucky to have had both my parents together, and still together, and they still love the hell out of each other even today. So maybe you and other women think that being with the abusive guy is normal (hence you think that's what a "relationship" is, and that you don't want a "relationship"), but it's really not normal. You had bad role models that's all.
I want a relationship eventually too; that's what it's supposed to be. Caring for each other, being vulnerable to each other, being there for each other when you're/they're angry or sad, listening to each other, etc. And I've seen it. And it's pretty obvious that's what you want too.