I don't understand why self-employed editorial pros don't find social media useful for getting work. And I'm an introvert.
I’ve long used LinkedIn, along with Twitter and Facebook, not to ask people for work or referrals but to post links to articles about editing, medical editing, and self-employment to make clear that I have a wide and deep knowledge of editing and to sound so interesting (in my commentary on the linked articles) that people think of me whenever they need a medical editor. This is not sales or bragging; it’s sharing knowledge and resources. And it works well for me. I get inquiries from potential clients and referrals from colleagues because of it.
It's not that you do sales pitches on social media. You just must be consistently present, in the particular venues that feel comfortable to you, and you share ideas and information about the things you know about in your profession. You don't brag, and you don't say, “I'm sharing this because I want you to see how smart and skilled I am.” You just share helpful stuff and answer questions about it when asked. You'll be remembered as that helpful person who has #editing or proofreading or indexing experience in, for example, astronomy or animal health or human rights or public education.
Remember, this technique doesn't work overnight. It's part of playing the long game of marketing.