fix(chat): fix quick app 2 starters (Issues #6507, #6510)

[Derikyan]

Description of changes

Starters settings or button names are not saved when there is chat history in preview
Changes made to starters settings should be autosaved

Intro text is added to message when "Immediately send prompt" setting is selected
Introduction text should not be part of message

Applicable issues

• fixes [Quick app 2.0][Starters]: Intro text is added to message when "Immediately send prompt" setting is selected #6507 , [Quick app 2.0][Starters]: Starters settings or button names are not saved when there is chat history in preview #6510

Checklist

• the pull request name ends with (Issue #<ISSUE_ID>) (comma-separated list of issues)
• I confirm that I don't share any confidential information like API keys or any other secrets and private URLs

PR title cheatsheet

<type>[optional scope]: <description>

1. type (required)
   • feat - A new feature
   • fix - A bug fix
   • docs - Documentation only changes
   • test - Adding missing tests or correcting existing tests
   • ci - Changes to our CI configuration files and scripts
   • chore - Other changes that are minor and/or not user-facing
2. scope (optional, current repo suggestions below)
   • chat
   • overlay
   • shared
   • sandbox-overlay
   • visualizer-connector

[Derikyan]

/deploy-review

GitHub actions run: 27274346206

Stage	Status
deploy-review	Success ✅
chat	Success ✅
overlay	Success ✅

[Derikyan]

/deploy-review

GitHub actions run: 27277510750

Stage	Status
deploy-review	Success ✅
chat	Success ✅
overlay	Success ✅