Wrap it in <form role="search"> to announce it as search, and always connect a label — even a visually hidden one — since a placeholder alone disappears once typing starts and can't substitute for it. Live suggestions get announced through an aria-live region or the combobox pattern.
A search field that shows suggestions as you type is really a form of combobox, but the intent differs. A combobox leans toward "pick one predetermined value," while a search bar is built around submitting a free-text query to a results page — you can submit a word that isn't in the suggestion list at all. It differs from a command palette in placement — a palette is a modal opened by a global shortcut, while a search bar is an inline element fixed to the page.