You are wondering how to support your son. It sounds to me like you are already doing so, by understanding that he is a person for whom change and transitions are difficult, who is very sensitive and who tends therefore to be a bit overwhelmed or anxious in social situations. You know that you were shamed for your social anxiety as a child and you are committed to not shaming your son. So you are doing wonderfully, and your caring for your son shines through.
I do have a few suggestions that may help.
1. For now, continue with the homeschooling meet up with your husband in their one on one morning. Don't force him to go by himself to the other homeschooling meetups.
2. Your plan to begin a morning with just your son while your husband has the baby is terrific. Its great to invite his friends for some of those mornings, but be sure to stay available, which will decrease his anxiety and increase the pleasure he gets from these social interactions. That will help him bond with these kids so that he begins to feel more comfortable at the meet-ups. But also be sure to use some of those mornings just for the two of you.
3. During your mornings alone with your son, help him explore his feelings about the meetups, and about his sister, and about strangers and new situations. See this as your time to do play therapy with your son. Treat this as "special time" -- here's a link on how to do special time with him:
Why do I suggest "play therapy" with you? Because you and his father are the people he most trusts in the world. Because you are uniquely equipped to help him with his fears and anxiety. And because you are the ones who need to help him reclaim his secure place in your family (in his own mind.)
What kinds of play will help him? Any play about his place in the family, about separating from you, about the meetups, about feeling shy or anxious.
Use stuffed animals to play "homeschooling meetup." Let one animal be anxious and worried, and hang back. But then find his courage and be happy engaging.
Do similar roleplays with a family that has a baby who is increasingly mobile. Don't worry if the baby gets cast out to see or lost. Expressing his worries and jealousies through play is much better than internalizing them.
Switch roles. You be the frightened one, and let him be the wise, brave one. Ham it up and get him giggling. Invent all kinds of situations -- meeting new people (pretend you're meeting his Teddy bear for the first time), getting ready for a new event, or for the meetup. Every time you do this, and he gets to giggle about you being so silly to be so anxious, he will be shedding some of his anxiety. (Obviously, you have to find the sweet spot where you ham it up and wink at him, so he knows you aren't REALLY so anxious. Otherwise, he will take you seriously, and that is no laughing matter.)
4. Get your hands on a copy of Tamar Chansky's book Freeing Your Child from Anxiety: Powerful, Practical Solutions to Overcome Your Child's Fears, Worries, and Phobias. This will be a great resource as your son gets older, and is also a great resource for you.
5. Help your son cry about all this. He has a lot of feelings that he needs to express, that are worse since the arrival of the baby. If he stuffs them down inside, they make him more anxious and fearful. What he needs is a chance to cry and get those feelings out. Your loving, compassionate presence makes him feel safe, which will help those feelings bubble up. They may emerge as anger, but right under the anger will be his fear and upset. He doesn't really need to talk, and neither do you. Just stay with him, hold him if he will let you, and keep reassuring him that he is safe. I think you'll find that after a good cry he'll be a lot more at ease.
6. Find someone to talk to about this. Your own anxiety about your son is completely understandable because of your past. But it makes you anxious, which he probably picks up on. What's more, that anxiety makes it hard for you to help him. To loosen up about this issue, he needs your confidence in him. To offer that, you need to find a way to have your own worries be heard, so you can relax a bit about all this.
I hope this is helpful. Your son may have a tendency toward social anxiety, but your early intervention will help him enormously so that he does not have to suffer as you did. Most important, enjoy him. He's a wonderful boy, with so much more to him than this anxiety. He needs you to see how terrific he is and to keep this all in perspective. Blessings to you and your family!