My son is 2 1/2 also, and very verbally advanced for his age, and because of that he tends to be more social than a lot of the kids in his play group. I am a stay at home mom too, and we do play group things maybe once a week. He is only now starting to interact more with the other kids. He still does the parallel play thing mostly, and the other kids who are less verbal than he is, do it even more. I think because you missed those months of playgroup activities you didn't get to see the gradual development. Lots of younger kids are more outgoing than 2 1/2 yr olds, because they are thinking of the other kids as play toys. At least that is what I noticed in my group. Once they really start to play with toys and not each other, they just play along side each other.
Also, I think a bigger part of this situation is that you have a new baby. He is probably feeling insecure and like he is being pushed away from you. When you go to playgroup and the other kids are all playing side by side happily, yours is wanting to stay close to you because the new baby is close to you. But he still wants to play, he just wants it to be with you. Even if he isn't as clingy at home, I think it could be the new baby thing. I don't think your efforts are for nothing, I just think it is going to take a little bit of time for him to readjust to be off playing without you.
Some people are going to respond that he needs to see a professional and be evaluated, and some people are going to respond that that is ridiculous. (I'm guessing, just based on past posts like this that I have seen.) I don't think there is anything ridiculous about being concerned about your son's development and getting him any help he might need. So if you think there is something to look into based on his milestones and development, by all means talk to your doctor.
But based just on what you wrote, it sounds like it is just a phase. Just keep trying what you are doing. I don't think you should force a shy child to play with other kids, but unless he seems seriously upset at being around the other kids, I don't think encouraging him to play is bad. My son used to be much more tentative than he is now around other kids (he had a couple bad experiences with agressive kids) but by exposing him to other kids regularly without forcing him to play one on one with them, he is much more social now. Give him lots of encouragement and as much attention as you can, don't hole up in your house, and just keep an eye on how he is progressing socially. Good luck!