docs: update docs subproject readme

[medubelko]

The instructions were incorrect and out of date.

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• I've followed the contribution guidelines.
• I've signed the CLA.
• I've successfully run make lint && make test.
• I've added or updated any relevant documentation.
• In documents I changed, I added a meta description if one was missing.
• I've updated the relevant release notes.

[Copilot]

Pull request overview

Updates the documentation subproject README to reflect the current (manual) process for updating the embedded Sphinx Stack configuration, replacing outdated automation-based steps.

Changes:

• Replaces the removed/obsolete “run update script” workflow with a “diff relevant files and copy changes” workflow.
• Consolidates dependency refresh steps and adds a final verification reminder against the Sphinx Stack changelog.

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[medubelko]

@jahn-junior I had another look, and felt it needed more elaboration.

[jahn-junior]

Question before I do another pass:

Are we writing these instructions primarily for the craft apps or Starbase itself? If it's the craft apps, is updating only the docs files something we see ourselves (or other contributors) doing?

I ask because I assumed we'd be most commonly incorporating tooling changes in our routine Starbase merges.

[medubelko]

Are we writing these instructions primarily for the craft apps or Starbase itself? If it's the craft apps, is updating only the docs files something we see ourselves (or other contributors) doing?

It's for the craft apps. So far the subproject has updated much more frequently than Starbase merges take place. This is a record of the goal that others can pick up.