[9.0] add system message in copy conversation JSON payload (#212009) (#212071)

# Backport

This will backport the following commits from `main` to `9.0`:
- [add system message in copy conversation JSON payload
(#212009)](#212009)

<!--- Backport version: 9.6.6 -->

### Questions ?
Please refer to the [Backport tool
documentation](https://github.com/sorenlouv/backport)

<!--BACKPORT [{"author":{"name":"Arturo
Lidueña","email":"[email protected]"},"sourceCommit":{"committedDate":"2025-02-21T12:48:15Z","message":"add
system message in copy conversation JSON payload (#212009)\n\nCloses
#212006\n## Problem\nDue to
#209773 we no longer add\nthe
system message to the output from the \"Copy conversation\"
button.","sha":"4783925e567681d1d2f9410e18ffa24050e4b69a","branchLabelMapping":{"^v9.1.0$":"main","^v8.19.0$":"8.x","^v(\\d+).(\\d+).\\d+$":"$1.$2"}},"sourcePullRequest":{"labels":["release_note:fix","v9.0.0","Team:Obs
AI Assistant","backport:version","v9.1.0","v8.19.0"],"title":"add system
message in copy conversation JSON
payload","number":212009,"url":"https://github.com/elastic/kibana/pull/212009","mergeCommit":{"message":"add
system message in copy conversation JSON payload (#212009)\n\nCloses
#212006\n## Problem\nDue to
#209773 we no longer add\nthe
system message to the output from the \"Copy conversation\"
button.","sha":"4783925e567681d1d2f9410e18ffa24050e4b69a"}},"sourceBranch":"main","suggestedTargetBranches":["9.0","8.x"],"targetPullRequestStates":[{"branch":"9.0","label":"v9.0.0","branchLabelMappingKey":"^v(\\d+).(\\d+).\\d+$","isSourceBranch":false,"state":"NOT_CREATED"},{"branch":"main","label":"v9.1.0","branchLabelMappingKey":"^v9.1.0$","isSourceBranch":true,"state":"MERGED","url":"https://github.com/elastic/kibana/pull/212009","number":212009,"mergeCommit":{"message":"add
system message in copy conversation JSON payload (#212009)\n\nCloses
#212006\n## Problem\nDue to
#209773 we no longer add\nthe
system message to the output from the \"Copy conversation\"
button.","sha":"4783925e567681d1d2f9410e18ffa24050e4b69a"}},{"branch":"8.x","label":"v8.19.0","branchLabelMappingKey":"^v8.19.0$","isSourceBranch":false,"state":"NOT_CREATED"}]}]
BACKPORT-->

Co-authored-by: Arturo Lidueña <[email protected]>

Author: kibanamachine

x-pack/platform/packages/shared/kbn-ai-assistant/src/chat/chat_body.tsx

@@ -255,7 +255,8 @@ export function ChatBody({
     const deserializedMessages = (conversation.value?.messages ?? messages).map(deserializeMessage);
 
     const content = JSON.stringify({
-      title: initialTitle,
+      title: conversation.value?.conversation.title || initialTitle,
+      systemMessage: conversation.value?.systemMessage,
       messages: deserializedMessages,
     });