My first thought was try not to set yourself with expectations. Next, my son just joined a group of people who have mental health challenges...this group goes out and does social activities together...bowling, shopping, movies etc...check in your area perhaps for....I'm in CT....this is a local resource, maybe your therapist could help you find a resource similar....my son has case management with the same agency for social activities...they are helping him transition to an independent life...I've done as much as I can as a Mom....there are just things I can't teach him...life lessons of falling down and getting himself back up again, not relying on me. https://ct-asrc.org/social-and-recreational-programs/

Consider what you believe are your strengths in a relationship and how and who that would support. Don't let folks steer you into only running with "your own kind", especially if you require support and affirmation from someone with less the same qualities as you have, who might serve as an outlet to experiences you have trouble engaging in own your own. Create or seek help composing a profile that presents your personality, interests and expectations and place it on a free web dating site like plenty of fish (https://www.pof.com/) , and see what happens. Beware of scams, there are so many of those, especially on free sites, but having taken a look around the net myself, they do, on pof, seem mostly very real. I'm not a professional and I haven't spent hours getting to know you so I should defer to your counselor in terms of what pace should be best, but...there's an almost great movie, "Jane Wants a Boyfriend", full of neurotypicals with great intentions but a rather narrow sense of what is appropriate for or within the grasp of an atypical, and who think an atypical can't necessarily expect to gain the same comforts that a typical can. You know that's nonsense and that you deserve to script the story of your life with all the advantages and experiences that the rest of society enjoys. Maybe try to be a little aggressive with the first steps you might propose to take, when planning with you counselor and push a little harder to see which of those they might endorse. If you're sure you're ready and they're sure you're not, maybe it's time to seek a second pro opinion. Maybe a counselor's with Asperger's opinion.