a partial solution:

if('BeforeInstallPromptEvent' in window)
    alert('Chrome-style PWA install experience supported!');
if('standalone' in navigator) // only available on iOS - but also on alternative browsers on iOS without Add-to-Homescreen support
    alert('iOS Safari-style PWA Add-to-Homescreen maybe supported!');

Open problems:

• avoid false positives on iOS - if you could accept using the user agent for that, you could use navigator.userAgent.match(/(iOS|OPT|Brave|GSA|DuckDuckGo|Snapchat)\//) to detect most alternative browsers; For explanation: iOS in the regex should detect CriOS|FxiOS|EdgiOS|OPiOS (Chrome/Firefox/Edge/Opera mini); Does anbody have a way to detect alternative browsers on iOS without using the user agent?
• it does not detect Firefox on Android; and I don't know if other browsers based on Firefox for Android support PWAs (e.g. QuantMobile, PrivacyWall, Fennec, KAIOS - all tokens that appear together with Firefox and Android in the user agent string)

Addition (untested & unreliable): I did some more research:

• A sure sign that you are in a webview on iOS is (or was?) that navigator.mediaDevices.getUserMedia or maybe navigator.mediaDevices is undefined. But I also read that Apple implemented it some months ago - so there will be webviews for which this isn't true.
• Another hint might that if navigator.doNotTrack is undefined, it could mean that you are in a webview (or that Apple decided to remove this deprecated property from Safari...)