I know for PWA's on Chromium-based browsers (at least on Android) you'll either get a bottom bar with an app store-like listing (most commonly seen on sites like Xitter) or a prompt right below the omnibox with an install prompt.

It's inconsistent though, since some sites and services with PWA support that don't have the manifest included somewhere in their code won't have either show up. And don't even get me started on iOS' "support" outside of the EU.