Credentials stay in this browser only. The default host relays to your broker over port 443, because some networks — iCloud Private Relay among them — block the broker's own port and the connection simply times out.
On iPhone, a page added to the home screen keeps its own separate storage — these details have to be entered again inside the app.
No units yet. They appear as soon as one publishes its status.
If it connects in the browser but not in the installed app, run this inside the app — an installed page has no console to look at.