It's a billion dollar question, how to make friends as we get older. And I think hard to answer as everyone is different and people value different things in friendships.

If you say you do not come over as empathetic, then try and change that? Sometimes people do not want to hear solutions to a problem (something I try to do too) and would rather just be able to sound off and hear sympathetic noises. Perhaps you could try working on that? And also a bit of your confidence - if you felt completely uncomfortable with the other mums, perhaps try and hide it a bit. You may come over as stand-offish, if you know what I mean. It stops people approaching you. I should imagine too, that on the surface, that most mum's at a playgroup just talk about their children. Am sure if you went back for a few weeks, you'd start to get to know them a bit more.

The other thing I try to be is light hearted and friendly, with a smile on my face. I do find friendships harder as you get older tho, as everyone has their own life, families, old friends, schedule etc, and it seems that there's not always room for another.

Good luck and hugs.