Rehydrate an expired Expert conversation instead of disabling chat

A user who stays in the Expert chat for more than 30 minutes hits the conversation expiry: "Your conversation history will expire soon" followed by "Your conversation history has expired. Chat is now disabled. Click Start Over to begin a new conversation." During onboarding this is a dead end: the funnel has no navigation, and asking a brand-new user to start over throws away the intake they just went through.

When the history expires, rehydrate the chat with a new conversation id transparently: keep the visible messages in place, swap the id underneath, and let the user simply send their next message and go forward. Never disable the input or ask them to start over.

The same applies to the normal Expert channel: remove the expired-chat Start Over dead end there too and renew silently.

Done when: a chat left open past the expiry keeps accepting messages, in onboarding and in the regular Expert drawer, with no expiry banners and no Start Over prompt.

Start by tracing conversation expiry handling in the onboarding Expert chat and the regular Expert drawer. Follow how the conversation id, expiry banners, disabled input, and Start Over prompt are managed. Done means both entry points keep visible messages, renew the conversation transparently, and accept the next message without banners or a Start Over prompt.

Written by the indexing model from the issue text.