My DS1 was a limited eater as a toddler/preschooler and at 14yo he eats most things except raw veg and things that having braces prevents.
No way at 4 he's eat soup or curry... so I don't think she's as limited as you think.
Be mindful that 50 years ago the range of food in an average house was 1/3 of what it is now, and 100 years ago it was 1/6th. In 1944 a 4 yo ( my Mum) in an Australian familywould eat porridge for breakfast a cheese sandwich and a meat and potatoes and one veg evening meal with fruit and custard... that was a daily diet, day in day out. Biologicaly a 4 yo has between double an 10 times more taste buds than an adult, so flavours are tasted stronger.
What worked for. Us (and worked incredibly well)
1) only expect one new food to be accepted every month (on average)
2) 1 simple rule, we eat what we want from the plate with no comment or drama from parent or child
3) 5 things on the plate. Starting out it was 3 things likely to be eaten, 1 possibly eaten and 1 new thing. Stick with rule 2 in the early days esp parent. 5 things could be some bread ( never enough to fill up on) cheese and apple as the will eat, then green beans as the possibly eat, and then thee other item was what DH and I were eating, or some nights it could be pasta, cheese and lettuce as the will eat, bolognase sauce on the side as the may eat and tomatoes as the not eat.
4) extra of a preferred food was judged based on the time, was it likely they might try something more on the plate or were they tired and just needed more food
5) never make it a drama, good quality healthy bread and water can be enough to live on and they'd never starve
Over time I worked out DS1 needed exposure to foods about 100 times before he'd embrace them.
Over time I changed it to 1-2 will always eat, 1-2 sometimes eat, and 1-2 new foods based on what DH and I were eating.
I had a routine where 2 nights I would do things I knew I'd get 100 happiness from them - sausages and home made chips, nuggets and home made chips, then one night was a picnic night with a pick your own food from a platter, the other 4 were meals that I wanted them to take on board, standard ones like bolognaise or lasagna, strip fry ( which I did deconstructed, with no sauce, so cooked each part separately, then tossed it together for DH and me, but served the boys one pile of meat, rice or noodles, and different veg piles.
I've never been a parent to use a time out/ naughty step because I was a child that would become more stubborn with being punished and it disconnected me more from my parents and I didn't want that. I was a limited eater as a child too and I know I'm not now, so I chose to make it a journey rather than expect results now, I did some research to understand the information above about taste buds and history and with that I was able to be calm and grasp that it was my lack of understanding that led to frustration rather than a difficult child. By 8 DS1 would eat what's on his plate no matter where we were. My nephew who was a great eater at 4, at 13 is a much more limited than either of my boys and My mum admits I was her most limited eater as a child and my brother her best eater, but now it's totally the opposite... my brother is a picky adult... he eats everything he did as a child, but given he's 51, the variety from then is less than half what it is now... so his diet is more limited than mine KWIM.
A really good way to look at it is look at how well she is reading and doing arithmetic at the moment... it's pretty basic and limited... by the time she can read Harry Potter and do her 12 times table... then expect her to pretty much eat the variety you do, until then make sure you offer up the good choices, but also the bread or naan that will feed her...over time she will eat more... they generally do.
