Appium is suited quite well for testing a PWAs and I use it for this purpose on a daily basis. You will find that, when running on a device, there is not a whole lot that makes a PWA special; it is just a web page running in a special web browser (called a “context” in the Appium world) that is wrapped by the native app.
With that in mind, Appium is just a connector between your test scripts and your device that runs the app so the details will depend on what test script technology you choose. We use Selenium in my shop and the tests are written to be run against a webpage regardless of environments. The only thing that is different when using Appium/Devices is that the first step of the test needs to “switch contexts” so that the automated script commands are sent to the “in-app browser” that the PWA is running in.
Here are some write ups: