Short answer - no I don’t think headboard shape needs to match side mirrors for best look.

More thoughts - trying to do that might make the search for headboard a long one. I’d find the headboard & nightstands you really like & only then consider how they’ll look with the mirrors. The style might matter more than anything -i.e. an ultra modern or minimalistic style probably won’t look great with these detailed mirrors. But, if the mirrors reflect the basic style that still appeals to you, there’s a better chance a new headboard & nightstand set you like will blend nicely with the existing mirrors.

I think it would look better if the mirror and headboard were not the same shape. Contrast is a wonderful thing and will make the mirror shape feel even more special.

I also don’t think they need to be similar.

You have the mirrors..you like them…they could possibly be used elsewhere..choose the bed set you want …and decide at that point..where to use them