Firstly, you are not failing your children! You are here seeking advice and support for you and your emotions, you are seeking appropriate support for your children, you have guided them through a transition from nursery and into school and you have planned ahead and organised a birthday party for them. Those all sound like successful parenting to me.
I also recognise those feelings of a loss of identity and no longer feeling I fitted in anywhere.
In my experience, it does improve. For me, it took probably 5 years - but I always was a slow learner! I think it started to improve when I accepted that I wasn't ever going to fit in with the school gate crowd (and also sadly, that some of my family would never 'get it').
That acceptance took a while, and took a supportive, understanding therapist to help me reach it. I almost had to grieve; grieve for the 'easy' children I didn't have because of their level of trauma, grieve for the easy friendships that didn't happen because I had to focus on my children when they tumbled stressed and tired out of the school doors - no playing in the park while I chatted with other parents. I had to grieve the friendships I lost because I could no longer give them the time they needed - or even if I did I was parenting/living on a different planet somehow and there was a huge disconnect. I had to grieve for the family members who became critical, divisive or just not interested. I also grieved for my children - because my grief made me connect with all their losses and truly see how much they had lost. That was painful - but ultimately helped to strengthen my bond with them.
Once I had accepted our reality, I started to find a new identity for myself and that gave me a confidence I hadn't felt for years. Yes, that identity was initially mainly as a harried, stressed Mum constantly pushing for support of one kind or another - but it gave me a sense of purpose and that's what I needed at that time. Perhaps that may be a starting point for you, accepting 'where you are'?
From that point, I started to make new friends - not all adopters, not all even parents and some who I met in the strangest situations! Not many admittedly - but they are true friends who understand my children, me and our situation.
I also agree with trying to carve out little bits of time for you - a regular meal out with a friend, a weekly trip to the library, a short daily walk; whatever works to relax you. My children still regularly moan about how long I take in the shower. It's one of my favourite things; I stand in the shower every morning and somehow that pulsing water helps enliven me for the day ahead - so I make the most of it!
I hope you can feel reassured that many of us have felt similarly to you and I hope you start to find your identity and confidence again.
(As an aside, what is is with so many adopted children having birthdays in December and January? Talk about adding in stress and pressure!)