I am unclear what you are reporting.
Can you log into the Apple developer portal?
As this is centrally involving some old iPhone of yours that you found in a drawer, is the iPhone or its display hardware possibly simply wonky?
As for web apps, saving a web page to your home screen is a function provided by Apple. That can then provide additional functions, including notifications. Here is a mobile website web app provided by the US NOAA National Weather Service: mobile.weather.gov
You can “save” that web page to your iPhone or iPad home screen if you want, and it then works mostly like an app.
On iPad, the web page save (highlighting added) available from the Sharing menu looks like this:

A whole lot of apps are also at least partially implemented as browsers, as well. The Apple Store app is one such app. Many apps providing a catalog of items or a gallery or such will be.
As you have already discussed this—whatever this might be, and that is quite unclear—with Apple, and have undoubtedly followed their suggestions for re-securing your Apple ID, then it is unlikely anything further that can be added to those recommendations here.
Per Apple:
… If you think your Apple ID has been compromised - Apple Support — re-secure your account
… Personal Safety User Guide - Apple Support — there’s a PDF of that guide at the bottom