<div id="spisok">
<div id="elem1">
<p id="elem1p">
<br>Элемент 1
<button>Кнопка</button>
</p>
</div>
<div id="elem2">
<p id="elem2p">
<br>Элемент2
<button>Кнопка</button>
</p>
</div>
....
<div id="elemN">
<p id="elemNp">
<br>ЭлементN
<button>Кнопка</button>
</p>
</div>
</div>
const result = Array.from(
document.querySelectorAll('#spisok > div > p > br'),
n => n.nextSibling.textContent.trim()
);
const result = Array.prototype.map.call(
document.getElementById('spisok').getElementsByTagName('button'),
n => n.previousSibling.nodeValue.replace(/(^\s+)|(\s+$)/g, '')
);