docs: add Server and client public APIs and Environment-specific Public APIs sections

[Gaic4o]

Background

Added content about environment-specific Public APIs.
Additionally, the ja Next.js documentation was outdated, so I updated it to the latest version.

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[Solant]

It looks like you also updated translations for other languages. Do you think it can cause issues with the translation dashboard https://lunaria.dev/recommendations/#keep-pull-requests-small ? Maybe we can split this change into several MRs so the translation dashboard is happy, and it is easier to test

[Gaic4o]

It looks like you also updated translations for other languages. Do you think it can cause issues with the translation dashboard https://lunaria.dev/recommendations/#keep-pull-requests-small ? Maybe we can split this change into several MRs so the translation dashboard is happy, and it is easier to test

Got it, that makes sense.
I hadn’t considered how this would affect Lunaria’s translation history.

I’ll split the translations by language into separate PRs for easier review.