When I was playing around with puppeteer in wsl2 it wouldnt run at all. What was missing were some required dependencies in my ubuntu distribution.
sudo apt install libnss3-dev libgdk-pixbuf2.0-dev libgtk-3-dev libxss-dev
after installing these dependencies in wsl2 puppeteer would run just fine.
Here's a demo script i used to check.
const puppeteer = require("puppeteer");
(async () => {
const browser = await puppeteer.launch();
console.log(await browser.version());
const page = await browser.newPage();
await page.goto("https://google.com");
await page.screenshot({ path: "google.png" });
await browser.close();
})();