Support Packet changes: Search backend added

[Combs7th]

@claude, Let's update the Mattermost Product Documentation to reflect the admin's product experience from Mattermost server v.11.1.1 onward captured via engineering PR mattermost/mattermost#34377

Focus the docs update on:

• What new search backend information is now included in the support packet
• Why this information is useful for admins troubleshooting search-related issues
• Any changes to what admins can expect when generating a support packet

Link to Support Packet documentation:
https://docs.mattermost.com/administration-guide/manage/admin/generating-support-packet.html

DO NOT suggest changes to the following docs pages:

• changelogs
• important upgrade notes
• version archive
• removed and deprecated features
• unsupported legacy releases

[claude]

Claude finished @Combs7th's task —— View job • claude/issue-8591-20251218-2353 • Create PR ➔

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Updating Support Packet Documentation ✅

Successfully updated the Mattermost documentation to reflect new search backend information in support packets from v11.1.1 onward.

Todo List:

• Read repository guidelines (CLAUDE.md) - No repo-specific guidelines found
• Locate and review current support packet documentation
• Research the engineering PR to understand search backend changes
• Update documentation with new search backend information
• Explain why this information is useful for troubleshooting
• Document changes to admin expectations
• Commit and push changes
• Provide PR creation link

Changes Made

Updated the Support Packet documentation (source/administration-guide/manage/admin/generating-support-packet.rst):

1. Added search backend type information from v11.1 in the v11.0+ tab
2. Updated the diagnostics.yaml file description to note it includes active search backend type information from v11.1
3. Added explanation of why this information is useful: helps administrators quickly identify which search backend (Database, Elasticsearch, or AWS OpenSearch) is currently active for troubleshooting search-related performance issues and configuration problems

The documentation now clearly communicates that admins can expect to find search backend type information in their support packets starting from v11.1, which will help them troubleshoot search-related issues more effectively.

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[cwarnermm]

This issue will be addressed via #8590