3.5 Year old behavior

[Itsybitsyminion]

I've been reading on other threads mums with older children with the same issues of separation anxiety, but my daughter is driving me insane and I am really concerned as reception year is coming and she will face another challenge of going somewhere bigger and new.
She has no siblings and was born at the start of COVID. If i talk about this with any doctor, he will say it's typical behavior of a COVID toddler. I can't think of ideas for making her feel more independent and detached from me.
She now in a pony riding club as we have to leave her for an hour and she can engage with the staff and ponies. we suggested dancing classes as well but because we are not supposed to stay during the class she doesn't want to go! She's been to nursery since she was 2 and childminder before.
She still throws tantrums when she has to go to nursery although after being there she loves it. She's very shy at birthday parties and takes a while to adjust to the new environment. She can even be that way with family. Constantly hiding herself around me. I can't be the one dropping her off at stay and play at her little friends house as she will cry and beg to go back with me (when the idea is to stay so I can go back to work) she still screams in the evening to sleep with me.
She can throw a tantrum/meltdown for over 20min sometimes out of nothing!
I am trying to teach her how to communicate her emotions rather than scream and many times kick or slap me and dad. She's not violent as such but she goes so angry and frustrated that she looks absolutely wild. I always saw her as a very independent and confident young child but recently she's been more and more like this. She's lovely at nursery, calm, smart and engaged in all activities. She has a little group of friends that will start reception in September and so my daughter will be left without this group as she is starting only next year. I am kind of hoping that it will improve her confidence as she will then be one of the oldest and having to make new friends... But also that will be another challenge she will have to face. I am lost and a bit emotional about all of this
Any advise and shared experiences are welcome. Thank you

There are a few things in there they sound like my DD, especially the behaving beautifully at Nursery and the tantrums. Have Nursery ever raised any concerns about her behaviour?

I would say that having tantrums for 20 minutes and kicking and slapping you isn't that usual at 3.5 and it might be a sign that she could use some additional support.

How does she score on this speech and language progress checker?

@SiouxsieSiouxStiletto thanks for your feedback. I done the test. It's a yes for all questions. Her speech is perfect and she's learning my home language as well. No concerns at all from nursery and they book regular one to one meetings as well to discuss the progress of the children with the parents. I raised my concerns with them and they do a sort of one to one therapy/exercises to help her how to name her emotions and hopefully be able to communicate them using words rather than with a tantrum... Only because I asked them to, not because they see by her behavior the need to do it. I am aware of how young she is and hopefully in a few months this is just a memory from the past but at the moment it's being a bit too much to handle. I see myself sneaking out to the gym close to her bedtime so her dad can take over, because if I am in the house I will be the one having to do bedtime as well. My DH works long hours and I believe more quality time with him would take some pressure from me but sometimes it's just not possible. The long full-on meltdowns and the clinginess is what keeps me wondering if there's something to be concerned about and will it ever end