Offer Reconnect, not Reload, while offline, and keep Chat drafts across reloads

The header's offline action now reconnects in place. Reload is offered
only after three reconnects fail in one outage, and Chat keeps an unsent
message in sessionStorage across any reload. Stop and Resume Chopin stay
usable during a blip and are sent once it is over.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>