I question if a stiff shoe really makes much, or any, difference. Even if your foot does flex a bit, the pedals are still going around exactly as fast and hard as you push them.

I sometimes ride with running shoes that are as flexible as slippers. Sometimes with stiff cycling specific shoes. Often at high intensity. I don't think I can tell a difference in speed per effort either way.

Don't overthink it. Just wear what's most comfortable.