Add new llm logger for debugging AI features

What does this MR do and why?

Adds a new logger and debugging statements for AI features.

Issue: https://gitlab.com/gitlab-org/gitlab/-/issues/409977

Screenshots or screen recordings

logging

How to set up and validate locally

1. tail -f log/llm.log
2. Set up your local instance for AI features
3. Test an AI feature like summarize comments
   1. Active it by enabling the feature flag: Feature.enable(:summarize_comments)
   2. Go to an issue with comments and press the "Summarize Comments" button (see video)

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this MR.

changed milestone to %16.0

added groupai framework maintenancerefactor typemaintenance labels

assigned to @nicolasdular

changed the description

added backend label

	1 Warning
	4052c546: The commit subject must contain at least 3 words. For more information, take a look at our Commit message guidelines.

	1 Message
	This merge request adds or changes documentation files. A review from the Technical Writing team before you merge is recommended. Reviews can happen after you merge.

Documentation review

The following files require a review from a technical writer:

• doc/administration/logs/index.md (Link to current live version)
• doc/development/ai_features.md (Link to current live version)

The review does not need to block merging this merge request. See the:

• Metadata for the *.md files that you've changed. The first few lines of each *.md file identify the stage and group most closely associated with your docs change.
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• Documentation workflows for information on when to assign a merge request for review.

Reviewer roulette

Changes that require review have been detected!

Please refer to the table below for assigning reviewers and maintainers suggested by Danger in the specified category:

Category	Reviewer	Maintainer
backend	Marcos Rocha (@mc_rocha) (UTC-4, 6 hours behind @nicolasdular)	Sincheol (David) Kim (@dskim_gitlab) (UTC+9.5, 7.5 hours ahead of @nicolasdular)

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Hey @mksionek, Do you mind performing a backend review for this merge request, please? :)

Thanks!

requested review from @mksionek

approved this merge request

LGTM @nicolasdular, just one question!

requested review from @jprovaznik and removed review request for @mksionek

@mksionek, thanks for approving this merge request.

This is the first time the merge request is approved. To ensure full test coverage, a new pipeline will be started shortly.

For more info, please refer to the following links:

• rspec predictive jobs
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• merging a merge request.

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