docs: sync merged Managed Postgres restructure (pg_clickhouse move, BetaBadge)

[mintlify]

Summary

Syncs follow-on commits from ClickHouse/clickhouse-docs#6279 (now merged): moves pg_clickhouse under Managed Postgres → Extensions, adds redirects for the old URLs, restores the missing FAQ context, and updates the BetaBadge on the migration overview to match the new convention.

This is a follow-up to the prior PR (#60) which ported the initial sidebar restructure and the new migration overview page.

Changes

• Moved integrations/connectors/tools/pg_clickhouse/{introduction,tutorial,reference}.mdx → products/managed-postgres/extensions/pg_clickhouse/….
• Updated slugs to /cloud/managed-postgres/extensions/pg_clickhouse[/tutorial,/reference] to match source.
• Updated internal cross-references in extensions.mdx, quickstart.mdx, and the moved pg_clickhouse files to point at the new file paths.
• Removed the pg_clickhouse sub-group from integrations/connectors/navigation.json (no longer cross-listed under Integrations → Data integrations).
• Added redirects in _site/redirects.json from /integrations/pg_clickhouse[/tutorial,/reference] to the new /cloud/managed-postgres/extensions/pg_clickhouse[…] slugs, mirroring vercel.json upstream.
• Updated products/managed-postgres/navigation.json so pg_clickhouse now nests under Extensions in the Managed Postgres sidebar (introduction, tutorial, reference).
• Updated BetaBadge on the migration overview to pass link, galaxyTrack, and galaxyEvent="docs.managed-postgres.migration-overview-beta".
• Applied heading-case fixes from upstream review commits (e.g. Getting Started → Getting started, Versioning Policy → Versioning policy) and the two duplicate-word typo fixes (any of of, the the).

Notes / ambiguity

• The Mintlify mirror still lacks dedicated clickpipes.mdx and migrations/faq.mdx pages — upstream uses these for its sidebar and overview's "After the migration" section. This PR keeps the overview's "ClickPipes" links pointing to the existing clickhouse-cloud.mdx (the closest equivalent in this repo) and omits the FAQ link. A future sync should bring those pages over.
• Upstream's vercel.json also added a redirect clickhouse-cloud → clickpipes. Not mirrored here because no clickpipes page exists yet in this repo to redirect to — the clickhouse-cloud slug remains the live target.

Context

Source: ClickHouse/clickhouse-docs#6279 (merged). This PR carries the four follow-on commits (3fb9527 move, 782d35e/6180f82/e4a5a0c heading review, a824d31 typo fixes).

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Note

Low Risk
Documentation, navigation, and redirect JSON only; no application or security logic changes.

Overview
This PR syncs follow-on documentation from upstream: pg_clickhouse moves from Integrations (Connectors → Data integrations) to Managed Postgres → Extensions, with slugs set to /cloud/managed-postgres/extensions/pg_clickhouse (plus tutorial and reference).

Redirects in _site/redirects.json map the old /integrations/pg_clickhouse paths to the new URLs. Internal links in extensions.mdx, quickstart.mdx, and the three pg_clickhouse pages point at the new paths; the Integrations nav entry for pg_clickhouse is removed and the Managed Postgres nav nests introduction, tutorial, and reference under Extensions.

The Managed Postgres sidebar is reorganized (e.g. data migration under Get started, pg_clickhouse under Configure → Extensions, monitoring under Operate & reference). A new migrations/overview.mdx compares ClickPipes, PeerDB, pg_dump/restore, and logical replication, with an updated BetaBadge on that page.

Minor doc polish on the moved pages: sentence-case headings, ClickPipes link tweak, and small typo fixes (any of of, the the).

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Cursor Bugbot has reviewed your changes using default effort and found 1 potential issue.

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[cursor]

BetaBadge component ignores all passed props

Medium Severity

The BetaBadge component at snippets/components/BetaBadge/BetaBadge.jsx is defined as a parameterless function (() => { ... }) that renders a static badge. The link, galaxyTrack, and galaxyEvent props passed here are silently ignored — no tracking fires and no link override takes effect. All other usages of BetaBadge in this repo pass zero props. The upstream component likely supports these props, but the local copy hasn't been synced to match.

Additional Locations (1)

• products/managed-postgres/migrations/overview.mdx#L9-L10

 

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