Enhance broken Jetpack connection detection.

Expected behavior

If a Self-hosted site is Jetpack connected and the connection is broken/not-fully-functional, the app should notify it to the user and possibly offer a way or guidance to fix the connection.

Actual behavior

If a Self-hosted site is Jetpack connected and the connection is broken/not-fully-functional, it seems the app continue to present the site as connected (in the JP app the dashboard is present and no note of a broken connection).

Steps to reproduce the behavior

This is coming from this internal slack thread p1705083454649729?thread_ts=1705052443.959929&cid=C0180B5PRJ4-slack-C0180B5PRJ4; I do not have steps to reproduce but seems worth to have it tracked for further digging and enhancement (more context might come from the slack thread to then track it here). When we look into it, makes sense to double-check if iOS has the same behavior.

Tested on [-], Android [-], JPAndroid / WPAndroid [23.9]

Start by reviewing the linked internal Slack thread for additional context and investigate how WordPress for Android determines whether a self-hosted Jetpack connection is fully functional. Establish a reproducible broken-connection case, check whether iOS shows the same behavior, and confirm that users are notified with guidance for fixing it.