I am sorry to hear you are so miserable. I don't understand what you mean about the suggestions people make about classes, church, rambling, hobbies, volunteering etc being unhelpful, as this is where we all meet our friends. You say people suggest things they wouldn't do themselves, but I think people suggest things that they actually have done themselves.
My best friends were made through work, hobbies, volunteering and baby activities. Not through family.
I don't think people have that "natural support network" you are talking about automatically. Even If you have a large family, it makes no difference to you socially by the time you are an adult. if you are having supportive, meaningful relationships with family members, you have worked on that, just the same as any friendship.
I have no regular contact with my family now, as none of the surviving relatives live in the same country as me.
Do you have a job OP? That is a good way to meet people, so if you are not meeting people, then maybe a different job might help?