JSFiddle - React, Tailwind, and code Playground

HTML

<div class='page__header'>
    <h1>title</h1>
    <div>
        <input>
    </div>
    <button>some button</button>
</div>

CSS

.page__header {
	display: flex;
	justify-content: space-between;
	background: lightgreen;
	
	 /* default rules; not necessary to include */
	flex-direction: row;
	flex-wrap: nowrap;
	align-content: stretch;
	align-items: stretch;
}

.page__header h1 {
	flex: 1 0;
}

.page__header button {
     order: 5;
}

.page__header div {
    /* align-self: left; */
    order: 2;
    position: relative;
    display: flex; /* NEW */
}

/* ADJUSTED SELECTOR */
.page__header input {
    min-width: 260px;
    padding: 0 1em;
    /* height: 100%; REMOVE */
    text-transform: uppercase;
}