[8.16] [ESS] [Serverless] Updates BYO LLM page (backport #6326)

[mergify]

Fixes #6276 by updating the bring-your-own custom LLM connector guide with a new model, screenshot, blog link, and several other minor changes.

Preview: Connect to your own local LLM (ESS) (Serverless)

---

This is an automatic backport of pull request #6326 done by Mergify.

[mergify]

Cherry-pick of 900040b has failed:

On branch mergify/bp/8.16/pr-6326
Your branch is up to date with 'origin/8.16'.

You are currently cherry-picking commit 900040b6.
  (fix conflicts and run "git cherry-pick --continue")
  (use "git cherry-pick --skip" to skip this patch)
  (use "git cherry-pick --abort" to cancel the cherry-pick operation)

Changes to be committed:
	modified:   docs/AI-for-security/connect-to-byo.asciidoc
	modified:   docs/AI-for-security/images/lms-cli-welcome.png
	modified:   docs/AI-for-security/images/lms-model-select.png
	modified:   docs/AI-for-security/images/lms-ps-command.png
	modified:   docs/AI-for-security/images/lms-studio-model-loaded-msg.png

Unmerged paths:
  (use "git add/rm <file>..." as appropriate to mark resolution)
	deleted by us:   docs/serverless/AI-for-security/connect-to-byo-llm.asciidoc
	deleted by us:   docs/serverless/AI-for-security/images/lms-cli-welcome.png
	deleted by us:   docs/serverless/AI-for-security/images/lms-model-select.png
	deleted by us:   docs/serverless/AI-for-security/images/lms-ps-command.png
	deleted by us:   docs/serverless/AI-for-security/images/lms-studio-model-loaded-msg.png
	deleted by us:   docs/serverless/AI-for-security/llm-connector-guides.asciidoc

To fix up this pull request, you can check it out locally. See documentation: https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/reviewing-changes-in-pull-requests/checking-out-pull-requests-locally

[github-actions]

A documentation preview will be available soon.

• 🔨 Buildkite builds
• 📚 HTML diff
• 📙 Preview page

Request a new doc build by commenting

• Rebuild this PR: run docs-build
• Rebuild this PR and all Elastic docs: run docs-build rebuild

_{run docs-build is much faster than run docs-build rebuild. A rebuild should only be needed in rare situations.}

_{If your PR continues to fail for an unknown reason, the doc build pipeline may be broken. Elastic employees can check the pipeline status here.}

[benironside]

run docs-build