Is this speech delay in a 24 months ?

Yes which is sometimes described as echolalia. Like the PP's brother ( and Einstein) who didn't speak till 3 then full sentences. Your DD sounds fine, as long as she is using her language in context and there is spontaneous language not just learnt or repeated words and phrases it is probably fine. I was just questioning the assertion that echolalia and use of learnt phrases are stages in typical language development.

Ummm I don't think this is completely true. Repeating words is normal- it's all about whether they understand what they are saying and are using words and phrases in context. Google gestalt language acquisition.

Sounds similar to my dc when they were 2.
They had their hearing tested as were referred there as part of SALT pathway. Now wearing a hearing aid and their speech really improved.

What is her spontaneous/self generated language like ? Is she regularly engaging with you to get your attention and to tell you things (even if at very simple level) ? Will she tell you about what she is seeing and doing as well as just requesting for toys/food etc ? Again could be at very simple level not full sentences

Understanding what/where/who questions is more of a 36 month expectation and actually retelling past events nearer 4th birthday.

She's 2. Sounds entirely normal.

Few 24 month olds would be able to answer a question like 'what did you do today?'
I say that as a childminder/nursery nurse of 20+ years who has worked with 100s of 2 year olds.

She doesn’t have to go to nursery at 2. But does she gets lots of time with other children her age to play with, like toddler groups and play dates?

I wouldn't have thought many 24 month olds would be able to answer 'what did you do today?' - it requires more of a concept of time?

I think you are 100% overthinking it. It's never a good idea to compare too much to other children as they all develop different skills at different paces - as long as she's progressing it is fine.

This sounds like the system working to me. It's good that the more generalist professional erred on the side of caution and referred to someone more expert. The expert is not worried, great.

She sound leaps and bounds ahead of my child who was referred for speech delay at age 2, and marked as behind but not enough for any intervention. Maybe she just doesn't understand why you're expecting her to randomly choose between bunny and dolly. Narrate what she is doing rather than quizzing her, vocalise your thought process as you choose between your trainers and your wellies. By all means keep an eye on her social understanding but I wouldn't worry or pursue SaLT on the basis of what you've written here.

Loving closed choices.

If the finds the responsibility of making choices too hard you could turn it around and say "I was wondering whether to give you a chocolate biscuit or a plain biscuit?". Then she's not responsible for the choice. This is probably more appropriate for slightly older children though.

My boss also does this. I can offer 2 different approaches and their response is 'yes'. It's annoying but generally during to lack of listening and attention.

I would have thought that they can answer simple questions at 24 months as well (not just following very basic instructions). Mine was able to do these things at just turning 3 (following basic instructions, pointing to body parts etc) and we were told at an assessment at 36 months that DC has a delay of about 1.5 years.

Agree with PP. Model language, don't ask open question and offer choices. That often helps a lot too.

can she respond to questions like: 'banana or apple?', can she correctly respond to with yes/no to question like 'more milk?'

So if you can see that she can do all of those things and more why on earth would you think she's delayed? I don't understand. As I said before I've got a 28 month old who has no words at all. Your little one sounds really advanced to me. I'd stop googling if I was you because you're looking for problems where there are none

Rather than ask 'What do you want, or which one ? ' expand that and ask
'Would you like a plain biscuit or would you prefer a chocolate biscuit ?'
Then she can copy what you said and pick the option she prefers 'chocolate'

Likewise when asking 'what did you do at nursery today?' add some options of what she might have been doing 'did you play outside, or did you do painting or did you do some dressing up?, and then pause for her reply, and she'll likely pick out something from what you've said to use in her reply.

Won't take long and she'll soon pick up on what you've asked with her own replies.
Then once at school you'll start getting the reply 'Nothing' 😂

Child has not been assessed by SALT and a HV will have no clue about disordered language development though...

It's not so much the amount of words but the receptive language which is more important at that point.

OP, her understanding sounds slightly delayed. Can you self refer to SALT for an assessment? I had a child with a number of words at that age who was able to follow simple instructions but not able to understand language beyond that. We also had the scripting/echolalia. HVs are unfortunately notoriously poorly trained to understand such a differentiated language development. Our HV blocked referrals for over a year. In the end, I got referred via GP.
You will probably get a lot of 'dont worry, the develo all differently' responses here but most posters have no real life experience of brining up a child with a language delay/disorder...I would listen to my gut here.

Also, had the heating been checked? Can she hear well. This is usually a first step.

It's very hard to assess at this age - and even a speech development expert would need to spend several sessions with your dd to even begin to know if there was an issue or not . The closest second to this option is to try to observe the speech of her peers - can they do and say the things you are concerned about ? I know many people say 'don't compare' and 'they all develop differently and it's all fine' but these people have no real experience of parenting a child with developmental challenges and they just think they are being helpful and re assuring. Also people tend to be very cautious about expressing agreement that there could be a problem with a child's cognitive and social development in a way that they would not be if the issue was physical - if your dd had a raging temperature, they would not say 'oh in the old days no one bothered about fever, all my kids had extremely high fevers and i did absolutely nothing, and they are all fine now', they would advise medical attention. Unfortunately, it's extremely hard to get any professional input from an NHS speech therapist, even if your dd was completely non verbal, they would put you off til 'later'. If you have a niggling concern, it might be worth asking around about a private assessment. Or look online for Hanen resources - 'It takes two to talk' to get advice on games and strategies to enhance language development in young children.

All that means is she wants both.