docs(python): Rename Getting Started to Getting Started by Example

[proxence]

• I have read and followed the Contributing docs, especially the "First-time contributing?" section.
• This PR has content that I did not fully write myself.
  • I used AI and I have read and followed the Generative AI Contribution Policy.
• I have the experience and knowledge necessary to understand, review, and validate all content in this PR.¹

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This PR closes the first task of this meta issue: #5692

The issue linked above provides full context but for a rough summary, the following discussion #4853 led to an agreed upon new approach for what the documentation structure should be. Those changes were made within the Java docs via several PRs and this is applying that same effort to the Python docs in smaller, more reviewable, changes.

NOTE: This is the same PR as #9705, but I forgot to create the PR from a branch in my fork so I had to re-open to fix that.

Footnotes

1. Yes, I can answer maintainer questions about the content of this PR, without using AI. ↩

[MikeGoldsmith]

Thanks @proxence 👍🏻

[otelbot]

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