I was told we couldn't take something made at home because of allergens etc and they discourage sweets etc. So I was told the best thing is stickers.
At our nursery you can take in shop bought cakes (in original packaging) so any allergies can be catered for. The won’t accept home made. I usually take a big tray bake in and then some diary/gluten free cupcakes (whatever the supermarket has) as that pretty much covers most allergies.
At our nursery the kitchen bakes a cake for the everyone - not sure if you brought one in they’d let it be given to other kids, maybe if it was store bought but probably not if homemade