I [31M] am trying to figure out where my friend's [28F] head is at after a really awkward date(?) and night together.

I've been friends with this girl Sarah for two years. We originally met as co-workers. We've since moved onto better opportunities but still run in the same circles.
For almost all that time we've been "casual" friends. Like, I thought she was cool and liked hanging out with her and everything, but it was always just circumstantial, like we'd get invited to the same place by mutual friends or something. We never specifically planned on seeing each other, if that makes sense.
So it was a little surprising last week when she messaged me to ask if I wanted to hang out with her on Saturday night. It didn't even occur to me that she has my number. But I figured she was trying to get the usual crew together so I just told her I was down to hang out, and went to meet her at a bar where my friends and I frequent.
When I got there I found Sarah at a table by herself. When I pulled up I asked her if any of the others had arrived yet and she kind of awkwardly told me "Oh, actually you were the only one I asked." I was really surprised by that, since we never were that kind of close friends who specifically ask each other for one-on-one time, and I was getting kind of a "date" vibe at that point. In any case I just rolled with it and we had a good time.
She was asking me some personal kinda stuff, asking me about where I've lived and what I've done before moving into town for college, what things I'm into. Y'know, stuff that would be normal if it were a first date. After a few minutes I straight asked her "Hey, so is this a date?" She acted embarrassed and told me she just wanted to hang out with me because she didn't know me too well and thought I was cool. Still kinda suspicious about what her goal was, but I dropped the date talk and we had a fun evening together.
After we closed down the bar we were both pretty drunk, Sarah a little more than me. When we left I told her I could call her an uber if she wanted, or she was welcome to come sleep it off at my place (which is just a block away from the bar). She said she wanted to go to my place so we stumbled our way there.
When we got up, I figured the safest course of action was just to put her in my bed and go sleep on the couch. After I got her into bed I went out to the living room and she walked about five minutes after and told me she didn't mind sharing the bed. Thinking she meant she wanted to have sex (and not really knowing how I should respond to that) I just told her I thought she was a little too drunk for that. But she responded that it was fine and we could just lay together. All things considered my couch is not really comfortable so I took her word for it and joined her in bed, where she snuggled up on me. Was really feeling confused on what we were doing at that point. And then she drunkenly kissed my cheek before falling asleep.
The next morning after she finally woke up I handed her some coffee and just asked "Sooo....are we gonna talk about last night?" She was evasive about it and gave me an answer like "Yeah, but not now."
We went out for breakfast on our way back to her car, and it felt really date-like again. But she still claimed we were just friends hanging out. Later on after she left I got another message from her that just said she had a lot of fun and wanted to do it again soon.
Just as an aside I was over at one of our mutual friends (who knows Sarah a lot better than I do) yesterday and I kinda mentioned the experience with him (did not mention laying in bed together though) and he made a comment like "Dude, she's been asking about you a lot."
So, I guess I'm kinda confused. Was that a date we went on the other night? It seemed like everything for a successful first date was there, but she made a point of not letting me call it that. And she has been texting me (which she never did before) and has reiterated that she wants to hang out with me again. But it isn't a date.
So, is this girl trying to date me without actually saying she is dating me? Am I being completely clueless about this whole situation?
TL;DR Girl went on a date and slept at my place the other night, but insists we were friends hanging out. Is she trying to date me or am I misreading this situation?


Source.