`You're not connected to the internet` text should be gone once connection is restored

### What
It looks like the app gives the connection status feedback to the user only when they click `Log In` or `Sign Up`:
(also, `Internet` should start with a capital letter)

This can be improved by showing the red text depending on the connection status changes in real time. Even better would be enabling/disabling the buttons as done in Electron.

### Why
More transparent for the user.

Start with the macOS login and sign-up connection-status UI described in the issue and compare its behavior with the Electron app. Verify how the red offline message responds when connectivity changes, and consider the requested button state behavior; done means the feedback reflects the current connection and the text uses the requested capitalization.

Written by the indexing model from the issue text.