Clarifies EDOT SDK authentication using API keys

[alexandra5000]

What does this PR do?

Updates documentation to explicitly describe how EDOT SDKs authenticate with the Collector for central configuration using Elasticsearch API keys.

Explains required privileges and configuration for the apikeyauth extension, improves example clarity, and corrects previous references to resource settings.

Why is it important?

Helps users correctly set up secure and functional central configuration flows for SDKs.

Checklist

• I have read and understood the pull request guidelines of this project.
  - [ ] My code follows the style guidelines of this project
  - [ ] I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
  - [ ] I have made corresponding change to the default configuration files
  - [ ] I have added tests that prove my fix is effective or that my feature works
  - [ ] I have added an entry in ./changelog/fragments using the changelog tool
  - [ ] I have added an integration test or an E2E test

Disruptive User Impact

None

Related issues

• Closes #467

[mergify]

This pull request does not have a backport label. Could you fix it @alexandra5000? 🙏
To fixup this pull request, you need to add the backport labels for the needed
branches, such as:

• backport-./d./d is the label that automatically backports to the 8./d branch. /d is the digit
• backport-active-all is the label that automatically backports to all active branches.
• backport-active-8 is the label that automatically backports to all active minor branches for the 8 major.
• backport-active-9 is the label that automatically backports to all active minor branches for the 9 major.

[github-actions]

🔍 Preview links for changed docs

• docs/reference/edot-collector/config/authentication-methods.md
• docs/reference/edot-collector/config/default-config-standalone.md

[theletterf]

Let's get @hegerchr 's approval as well.

(Is this related to elastic/opentelemetry#487?)

[alexandra5000]

@theletterf Yes, it's related

[alexandra5000]

Hi @hegerchr could you please approve this PR? 🙏

[mergify]

This pull request is now in conflicts. Could you fix it? 🙏
To fixup this pull request, you can check out it locally. See documentation: https://help.github.com/articles/checking-out-pull-requests-locally/

git fetch upstream
git checkout -b auth-snippet upstream/auth-snippet
git merge upstream/main
git push upstream auth-snippet

[github-actions]

@Mergifyio backport 9.1 9.2

[mergify]

backport 9.1 9.2

✅ Backports have been created

• #11502 [9.1] (backport #11170) Clarifies EDOT SDK authentication using API keys has been created for branch 9.1
• #11503 [9.2] (backport #11170) Clarifies EDOT SDK authentication using API keys has been created for branch 9.2