I’d batch cook for him and let him just reheat whatever each night and cook more adventurous stuff for you - for now!
I’m vegetarian which people wrongly assume = overly Ltd boring diet!
My ex was same as yours, extremely fussy thanks to his parents totally pandering when he went through a picky phase at the age most children do. As a result when I first met him there were literally 6 things he would eat!
He didn’t cook either. When we married & moved in together I got fed up within the first week of cooking and eating pretty much same thing every bloody night!
I did what many on here are advised to do with children!
Made him get involved with choosing and cooking food, made him try at least one new thing a week PROPERLY - not a wimpy nibble followed by “eww nah don’t like that” and in that week it would be cooked different ways so eg we would discover he didn’t like a certain vegetable boiled but liked it roasted or stir fried.
By the time I was done with him he was much better, unfortunately with wife 2 (who in my opinion panders to him too) he’s regressed AND passed his fussy behaviour onto his younger kids.
If you don’t have dc yet but are planning to I’d definitely advise getting this knocked on the head before having dc.
It may seem a minor issue but it can have a major impact on a child’s development and health.
One of ex’s younger ones is on iron constantly because they’re always anaemic due to poor diet.
And don’t let him dictate restaurant choices either, most restaurants have some kind of bland offerings if he insists but it’s not fair expecting you to always miss out when you eat out.
The “allergy” sounds psychosomatic to be honest, most people with a true nut allergy would be ill enough to necessitate a proper diagnosis. Many other things in the items you mentioned that could have made him ill as a one off, not due to allergy but food poisoning etc
Barring genuine allergies/intolerance and eating disorders I consider it unacceptable to be fussy purely due to being unwilling to try new things.