Вы можете попробовать этот селектор или этот xPath:
'use strict';
const puppeteer = require('puppeteer');
(async function main() {
try {
const browser = await puppeteer.launch();
const [page] = await browser.pages();
const html = `
<!doctype html>
<html>
<head><meta charset='UTF-8'><title>Test</title></head>
<body>
<div class="Menu">
<label class="Kit__caption Header__username">Logged in as: BAF Agent</label>
<div class="menu-item">Help / FAQ</div>
<div class="menu-item">Submit Feedback</div>
<div class="menu-item">Sign Out</div>
</div>
</body>
</html>`;
await page.goto(`data:text/html,${html}`);
let div = await page.$('div.Menu > div.menu-item:last-of-type');
console.log(await page.evaluate(element => element.innerText, div));
[div] = await page.$x('.//div[@class="Menu"]/div[@class="menu-item" and text()="Sign Out"]');
console.log(await page.evaluate(element => element.innerText, div));
await browser.close();
} catch (err) {
console.error(err);
}
})();