AIBU to feel lonely and left out at school events?

Sorry you feel like this. I never made mum friends as I was working and not always at pick up and dc were often in breakfast club. Offer play dates but don't expect dates to be offered to you, as you'll only be disappointed.

So they are not kind or friendly so why keep trying ?

move on

Maybe your expectations are way off
i am in my second child through primary school and. Do not have any friends from it . Lots of Pleasantries and polite chit chat at parties and sports day but they are not my friends

also i find the mums who do pick up snd drop off every day ( i cant ) have a crucial extra 20-30 mins every day to build up chit chat into a friendship

also i find mums who are super friendly with each other other have connections outside school. Ie i know one group who bonded in the NICU - you can’t compete with that kind of bond ,often they know each other other from nursery or newborn pregnancy groups football gymnastics so have many years and hours more bonding time

the summer holidays are a good time to offer playdates and have chill conversations at handover but be careful of coming across as desperate

if i end my 14 years of primary school with one friend that will be a win

you sound down do you need to see the gp?

No advice but I share your pain!
At my kids school, most of the parents went to school together so have know each most their lives.
I've had to wait until their a bit older and I can have hobbies to start making friends. It's rubbish

Sorry you feel like this op. I wouldn’t try and get in with the group but continue to try and organise play dates on an individual basis and from there you may pick up friends. My DC are young adults now but I remember not feeling part of a group (AKA the cliques) but made some really good individual friends usually via my children’s friendships.

The groups and cliques were often, as described by my DC, the parents of “the cool kids”. Not for me. Just keep trying individually and you will get there. If you have time and I know you say you work try and get involved either with the PTA / school events.