I was in a similar situation as yours several years ago. A baby bunny came into my care that was only 3-4 weeks old. I was given the information that she had been weaned, and also was used to the veggies green leaf lettuce and carrots.
That first day, she was perfectly happy and comfortable being in a new home, not nervous at all, would run around and explore and flop out when tired, but she would not eat anything. No pellets, no hay, wouldn't drink water at all, bowl or bottle. I hadn't yet tried lettuce or carrots because I was reluctant to give it to such a young bunny regardless of being told she had it before.
Back then I didn't know you should feed the exact same brand and type of pellets to a new rabbit for the first couple of weeks while you transition them to a new pellet , or that a rabbit could be picky about different hays as my previous rabbits had always eaten and been fine with whatever type or brand I fed them. This was before I knew anything about rabbit health or the proper diet.
So I didn't know any of that even mattered to a rabbit. I didn't really know anything about syringe feeding rabbits back then, and making a pellet mush didn't occur to me because I thought she wasn't eating because she hadn't been weaned properly and wouldn't eat because she still needed milk. But she wouldn't swallow the milk I tried to syringe her. And I tried several different types of formula. No luck though.
We had fresh alfalfa outside, so I decided to try some. Score! She ate the little piece. But then she got an upset stomach with it that lasted for several hours, I think maybe because it was a young early growth and really rich, so I was scared to try anything fresh or different with her after that. Not knowing what else to do, the next day I decided to try the green leaf lettuce(NOT iceberg) because of being told she was used to eating it, and you know what, she gobbled it down!
So I started feeding more lettuce, and she ate it right up and it wasn't causing any mushy poop or digestive upset. So I just kept feeding her the leafy lettuce for the next week, not knowing what else to do. I kept trying to get her to eat pellets and hay, but she just wouldn't touch them. So I kept feeding leafy lettuce. This little bunny that was the size of a teacup, maybe 8oz max, and was eating a ton of lettuce each day.
Now, I would never recommend feeding any bunny just lettuce. It's not a proper diet, and could cause problems for some rabbits. But I was inexperienced then and was just focused on keeping this bunny eating. The lettuce was just a temporary measure while I tried to figure out how to get her to eat pellets and hay. And over the next week as I fed her lots of lettuce each day, she gradually started to nibble on her pellets, and eventually a little hay. Then by the end of the week she was eating a good amount of pellets and some hay, and I gradually reduced the amount of lettuce as she had more pellets and hay.
But no matter what I tried she wouldn't drink water. So I kept offering enough lettuce over that second week to provide the needed fluid intake, to make up for the lack of water drinking, to help balance out the dry food she was now eating. I did syringe some water(carefully), but that didn't get her drinking water on her own. I needed to get her drinking on her own.
Luckily for me I had a neutered buck that was a really easy going calm rabbit, and I decided to see how he would react to this baby rabbit, to maybe see if he could help her learn to drink. This had to be done very carefully, as I knew an adult rabbit could cause an injury if the reaction was negative. But he accepted her right away, and once she realized he wouldn't hurt her, she was glued to him. So I kept the two of them together for the next week, and he taught her how to drink like a proper rabbit. But I couldn't keep them together, as he was bonded to an adult doe I had.
All I can figure is my baby rabbit really wasn't properly weaned, and this was why she would only eat the lettuce. Because it's the only solid food she was familar with. With your bunny, in one photo, she does look like she may possibly be only 3-4 weeks old. If she is this young, this could explain why you're having so much trouble getting her to eat anything. Because like my little bunny, she wasn't weaned properly. Luckily you're a step ahead of what I had tried. You're syringe feeding a pellet mush, and this is working for now.
So the next task is trying to get her to start to nibble on the pellets. A few things you can try are making the pellet mush and offering it in a little dish, to see if maybe she will eat it on her own. This would save you having to syringe feed. If she will eat this, just make sure it's not left out more than a few hours to prevent bacteria and mold growth. If she won't eat pellet mush on her own, keep up the syringe feeds, then you could try different brands and types of pellets, as it may just be that particular pellet she doesn't like the smell/taste of. What brand and type are you feeding now?
Also trying different types of hay like third cut timothy, orchard, alfalfa, oat, meadow, etc. Baby rabbits tend to like a leafier softer cut of hay. Normally I would also recommend trying fresh grass(wide leafed like orchard, not small leafed lawn grass), but because of RHVD illness starting to affect rabbits in the US, this might be too much of a risk. So safest to stick with dried hay varieties, sourced as safely as possible.
https://wabbitwiki.com/wiki/Hay
https://www.chewy.com/b/hay-11094
https://shop.smallpetselect.com/
https://www.rabbitholehay.com/collections/hay
Because you were told she is used to lettuce, you could try feeding her a little of a leafy lettuce if you want(not iceberg). But start with a very tiny amount. If she doesn't have an adverse reaction to it(mushy poop, stomach upset, become lethargic), you could gradually increase the amount each day. But this all depends if the previous owner was actually truthful about this. Normally it's not recommended to feed baby rabbits veg/greens until older because their digestive microflora isn't adapted to these foods. Unless they have grown up eating them with the mom rabbit, then they've developed the necessary microflora from their mom.
With the drinking, because you're syringe feeding she may be getting enough fluids that way and that might be why she won't drink. So as she starts to nibble on dry foods, you'll need to monitor if that also gets her drinking on her own or not.
