Progressive Web Apps are lightweight alternative to native apps which saves you from the hassle of installing multiple apps from Play Store. While they might be not feature rich and fast as native apps, they get the things done. They are even installed as native apps showing up in drawer, but they actually run inside webview.
Though these PWAs are installed as apks but they aren't backed up by Google's backup system and therefore can not be restored on your new Android device, leaving you to install them again by visiting those PWAs website again. But that is going to change soon as Google is working on the ability to let you restore all the PWAs you have currently installed on your new device. According to the feature flag, this is for Android devices only
I spotted some commits on GitHub Chromium repo which gives us a hint of how its going to work. According to a comment in GitHub commit "Only one promo can be shown in one run to avoid nagging users too much. The PWA Restore promotion runs when we've detected that a user has switched to a new device but is leaving behind web apps on the old device. It promotes the idea that the user can restore their web apps from their old device (if they have any), and as such it is most effective when shown shortly after the first-run experience. It is therefore at the front of the list of promotions"
Here are two screenshots of the PWA restore UI -
The above comment talks about showing a promo card to a user if it detects that user is using a new device and had any PWAs installed on old device. After digging through some other commits related to the same feature, when a user taps on the promo, an UI will show up listing the PWAs which user had installed on old device and from there user can select and install them again.
The feature is currently in work and hidden behind a flag in Chrome canary version 121 - chrome://flags/#pwa-restore-ui.