[DOC] Publish the doxygen doc

[marcalff]

Publish the generated doxygen documentation.

• Define where to publish (opentelemetry-cpp pages, or opentelemetry-io)
• Update CI to publish when merging to the main branch
• Retire obsolete doc at https://opentelemetry-cpp.readthedocs.io/en/latest/

[github-actions]

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[Emre-KMZ]

Hi, I would like to work on this issue. This will be my first contribution. All sorts of feedback are welcome, sorry beforehand if i am going too out of track.

1. Where to publish

After checking other OTel repos what I've found is:

• The js repo is the closest reference: it generates docs using TypeDoc and publishes to GitHub Pages, it seems like a good idea to follow the same pattern + keep it consistent.
• opentelemetry-cpp already has a gh-pages branch set up (currently used for benchmarks only), so we can publish Doxygen docs there alongside benchmarks.

2. Changes here

• New workflow that triggers on push to main (or on release, I will be thinking about it).

3. Retire the old ReadTheDocs.

• Delete obsolete files.
• Make the old documentation page to point to the new documentation.

[Cloud-Architect-Emma]

Hi @marcalff I’d love to work on this issue. This will be one of my first contributions to OpenTelemetry, and I’m excited to help with publishing the Doxygen documentation.

My plan is to:
• Generate the Doxygen docs locally
• Publish them to the existing gh-pages branch (following the pattern used in other OTel repos)
• Add a GitHub Actions workflow to publish docs on merge to main
• Retire the old ReadTheDocs configuration and add a redirect/notice

Before I begin, could you confirm that publishing to the gh-pages branch is the preferred approach?

Happy to get started once confirmed.