Improve web push docs

docs/subscribe/installed-web-app.md

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+# Using the web app as an installed web app
+
+While ntfy doesn't have a native desktop app, it is built as a [progressive web app](https://developer.mozilla.org/en-US/docs/Web/Progressive_web_apps) (PWA)
+and thus can be installed on both desktop and mobile devices.
+
+This gives it its own launcher (e.g. shortcut on Windows, app on macOS, launcher shortcut on Linux, home screen icon on iOS, and
+launcher icon on Android), a standalone window, push notifications, and an app badge with the unread notification count.
+
+To install and register the web app in your operating system, click the "install app" icon in your browser (usually next to the
+address bar). On iOS Safari, tap on the Share menu > "Add to Home Screen".
+
+## Background Notifications
+
+Background notifications via web push are enabled by default and cannot be turned off when the app is installed, as notifications would
+not be delivered reliably otherwise. You can mute topics you don't want to receive notifications for.
+
+On desktop, you generally need either your browser or the web app open to receive notifications, though the ntfy tab doesn't need to be
+open. On mobile, you don't need to have the web app open to receive notifications. Look at the [web docs](./web.md#background-notifications)
+for a detailed breakdown.
+
+## Compatibility
+
+<!-- TODO: (Q4 2023) Safari 17 / macOS 14 Sonoma supports installable PWAs too -->
+
+Web app installation is supported on Chrome and Edge on desktop, as well as Chrome on Android and Safari on iOS.
+Look at the [compatibility table](https://caniuse.com/web-app-manifest) for more info.
+
+<div id="pwa-screenshots" class="screenshots">
+    <a href="../../static/img/pwa.png"><img src="../../static/img/pwa.png"/></a> 
+    <a href="../../static/img/pwa-install.png"><img src="../../static/img/pwa-install.png"/></a>
+    <a href="../../static/img/pwa-badge.png"><img src="../../static/img/pwa-badge.png"/></a>
+</div>