Three year old social skills alone count to assessment

[Bpeep]

I am posting it here ibstead of SN section for more response. My 3.5 year old son was referred by his nursery for ASD assessment, for lack of speech, no response to name, repetitive play and other joiningin l with other kids. They pointed out many more and we gave our consent to proceed with process. After many month now, his speech is good. He speak to request his need, to show things he had done, he complains if someone hurts him or if he is on pain. He tries to comment on things around around him. Some of his comments are like this:

look mummy, bug coming inside
Sunny day sun shining
Somebody knocking a door
I have four balloons on chair

His speech is improving day by day, concerns on his language skill is still he is not asking "why". Not able to speak about things he did in nursery. He doesn't know to talk about things that happened few hours before on the same day.

His play skills has not improved yet according to nursery. He is still playing alongside kids rather than with them. He is now playing with toys appropriately. He communicating well in nursery with his teachers.
My question is not paying with other kids and limited speech at nursery alone count to autism diagnoses? Have anyone gone through the same in your kids and what was the outcome. Did you do anything at home to improve their social skills.

Nursery staff are not experts and can only guide by what they see - they are able to compare with his peers. The fact that the nursery actually cares (many do not) and are concerned is positive - if there is something (this is a big if) they want to catch it as early as possible in order to be able to better support him, however, it is very possible (most times) that what they see is not autism. Playing alone and having a speech delay does not even come close to an autism diagnosis.

@Aladdinmum, Thanks for writing. A part of me says he is fine, a part of me worries whether he will be labelled too early before even he acquired the language to communicate properly. He speaks to us but not in nursery or with other kids in his class. That worries me a lot.