It is not supported on desktop Safari, on mobile Safari it is supported (actually mobile Safari introduced this input type).
On desktop Safari, or any other browsers that do not support this input type, what will happen is that it will be rendered as regular <input type="text" ...>. No problem whatsoever as long your users fill the date in the ISO format ('yyyy-mm-dd')
What I usually do to hint users using browsers that don't support date inputs is adding the placeholder, pattern and title attributes to hint how they should fill that field
<input wire:model.lazy="birthday" name="birthday"
type="date" required class=""
placeholder="yyyy-mm-dd" pattern="\d{4}-\d{2}-\d{2}"
title="Provide a date in the format yyyy-mm-dd">
Hope it helps.