Feature request: bookmark and restore greeting in `chat_restore()`

Feature request: bookmark and restore greeting in chat_restore()

Summary

chat_restore() currently saves and restores the ellmer client's turn history, but it has no support for the chat greeting. Apps that generate dynamic greetings (via chat_set_greeting() / the greeting_requested input) must implement their own persistence logic if they want the greeting to survive a bookmark restore.

Current behavior

chat_restore() serializes and restores the chat client's turns. The greeting — whether static (passed to chat_ui()) or dynamic (set via chat_set_greeting()) — is not part of that state. After a bookmark restore, the chat history is repopulated but the greeting area is empty. The greeting_requested input fires again, causing a dynamic greeting to be regenerated, which costs an extra LLM call and may produce a different greeting than the original.

Desired behavior

chat_restore() (or a companion API) should let apps save and restore the greeting text alongside the chat history, so that:

1. A previously generated greeting is re-displayed verbatim on restore (no extra LLM call).
2. Apps don't have to manage a parallel reactiveVal + onBookmark/onRestore pair just for the greeting.

Workaround

querychat currently works around this by manually storing the generated greeting in a current_greeting reactiveVal and re-applying it with chat_set_greeting() on restore — roughly:

current_greeting <- reactiveVal(NULL)

observeEvent(input$chat_greeting_requested, {
  stream <- greeting_client$stream_async(GREETING_PROMPT)
  chat_set_greeting(id, chat_greeting(stream, dismissible = FALSE))
  # ... capture the streamed text into current_greeting for later bookmark persistence
})

session$onBookmark(function(state) {
  state$values$greeting <- current_greeting()
})

session$onRestore(function(state) {
  greeting <- state$values$greeting
  if (!is.null(greeting)) {
    chat_set_greeting(id, chat_greeting(greeting, dismissible = FALSE))
    current_greeting(greeting)
  }
})

This is a reasonable amount of boilerplate, but it would be cleaner if chat_restore() handled it automatically — perhaps via a greeting reactive argument analogous to the client argument.

Start by reading the chat_restore(), chat_set_greeting(), and greeting_requested entry points, then compare them with the querychat bookmark workaround described here. Decide how greeting state should be persisted for static and dynamic greetings, and define tests or examples that verify verbatim restoration without another greeting request.