Broiler starter has higher protein, sometimes up to 24%. It isn’t ideal for chicks intended for laying to have that much, but if that’s all that was available, it’s suitable to feed them. Chicks intended for laying should have 18-20% protein feed in the first 8 weeks of life, and then 16-18% from 8-20 weeks, or until they start laying. Broiler chicks are programmed to eat all the time. They have an amazing calorie conversion ratio. Your laying chicks will not end up like big fat meat birds if they eat the feed for broilers.
I’ve been using broiler feed at 20% protein to feed my adult laying flock (which also has pullets, chicks, and roosters in it) since March. I provide free-choice calcium in the form of oyster shells and egg shells in a separate feeding bowl for the laying hens. They are all fine!
Edited to add: I’m feeding the same feed to my actual broiler chickens and can assure you they are humongous. I actually have chicks that are eight days older than the broilers, and they are still tiny (eight weeks old) where some of the broilers are bigger than my laying hens. They’ve all been eating the same feed.