We just got off the Wonder days ago
and our DD who is 7 has peanut and tree nut allergies. She was fine, no reactions and we ate in MDR and buffets. Overall the experience was good.
In the MDR our server always assured us when the bread course was okay and if it was not, they brought a separate basket of safe bread. They did not recommend she eat the corn bread on pirate night, because it had nutmeg, which is not a nut, but I read other stuff about the cornbread on the Fantasy (?) and I opted to have her skip it.
On the Wonder they did not ask us to order her meal the previous night. She had chocolate pudding most nights for dessert (which was a treat for her). The last night she had the caramel "flan" like dessert. I typically do not allow her to eat commercially made ice cream such as Edy's, Hood, Breyer's since none of those are made on dedicated lines and that is not within my comfort level so we did not inquire about the ice cream at the lunch buffet at Parrot Cay.
The MDR did not make her a special dessert, but I never asked.
Buffets each time I told someone that I wanted to see the chef. The chef would walk us through the buffet and tell us what was ok. Generally they would get it from the back if I asked. Embarkation day at Beach Blanket, the chef walked us through. There was mac and cheese on the buffet. I asked if she could eat it from the buffet or if we could get it from the back. The chef assured us it was fine (she was fine, but after that I got most food from the back).
On several occassions at Parrot Cay buffet and BB, the chef asked what she wanted and made it for her (mac and cheese, chicken tenders - these are the things she wants to eat anyway and I did not see at the buffet). I does take time though so you may have to wait. Sometimes they had to go to another part of the ship to get it.
One night for dinner we skipped MDR to watch a movie and had dinner at Beach Blanket. The Chef was awesome, brought her a fruit platter, mac and cheese, bread and a special chocolate cake (which she said was good, I did not try it). He did not want her to take food from the buffet itself. Same for one or two lunches at Parrot Cay (buffet), the chef took her order and brought it over.
Dessert - she had a lot of jello which was safe, not exciting, but safe. Cookies are not safe (I believe Nestle chips).
At breakfast the pastry "tray" is tricky as everything is together. The chef would bring her donuts (safe) from the back.
Sorry this is very long (it is fresh). Overall DD had a pleasant dining experience. I found you might have to press a little if you need something or are uncomfortable. The night she got the special chocolate cake I asked the chef if there was a dessert she could have and was happy he didn't come out with jello.
I didn't see a ton of peanuts (there was a peanut butter pancake offered at Tritons and some peanut butter cheese cake), but lots of other nuts (walnuts, pistachio, pecans) on the menu and buffets.
We do not avoid SOY so I can't help there.
ETA - I did have it noted on our reservation and did mention it whenever we sat down to eat. Although our serving team seemed very aware, I would occasionally ask if everything was ok for her that we were ordering.
Feel free to ask any questions.