What's the latest way of submitting pwas to the app stores?

Basically, yes, wrap it in a WebView. I'd need to see your mobile website to judge it better, but if it looks like a website, Apple might reject it. Your website really needs to look like an app to have some certainty of getting it through if your app only consists of a WebView.

At webtoapp.design we usually include some native components in the apps. Although they might not add functionality (just replaces some website components), they help get the app published.

I guess you'll have to decide based on your hourly rate whether it's worth it to tinker with some self-built solution or if you are also open to going with a finished product. I don't want this to sound too much like an ad, just expanding on the time save (because often you don't think about all the things in advance): - If your client decides he wants push notifications: A finished solution should already have support for that - For Apple, you'll also need to set up your Xcode developer environment and manage all the certificates and provisioning profiles (personally, I found that complicated when I started out). With webtoapp.design we handle all of that automatically (we upload a finished build to your developer account) - not sure if some competitors do that too.