Hi OP, the best way to approach these events is to be very supportive to yourself, give yourself lots of self compassion, and don’t expect anything from the other parents. If you turn up, stay positive and casual, and don’t judge yourself through others eyes, you won’t feel brought down by it.
A few tips:
You don’t have to be in those chatty groups. Take that pressure off.
Those people are not there to judge you and there will be lots of other parents feeling as you do.
If you say hi and wave then that’s great.
Focus on your friendships outside of that setting.
If there are other quiet parents there chat to them - don’t try to get in with the groups of people looking comfortable: leave them to it. And don’t judge yourself for not being the same. They might have had a long standing friendship, who knows.
If you need some more positive interactions in your life, seek it elsewhere such as MeetUp, evening classes, walking groups etc.
These things take time and you might find a surprise friend along the way amongst the school parents but if not, it really doesn’t matter.
You never have to judge yourself for not being observably in a group in the school setting. Bollocks to it.
Stay strong and don’t put yourself down 