docs: restructure Managed Postgres sidebar and add migration overview

[mintlify]

Summary

Port of upstream clickhouse/clickhouse-docs#6279: restructure the Managed Postgres sidebar into four functional groups and add a Data migration overview page.

Changes

• Added products/managed-postgres/migrations/overview.mdx — decision guide comparing ClickPipes, PeerDB, pg_dump/pg_restore, and logical replication.
• Restructured products/managed-postgres/navigation.json into four groups: Get started, Use it, Configure, Operate & reference. Data migration now sits next to Connection; Extensions is a nested group containing pg_clickhouse; Monitoring is a nested group.
• Surfaced pg_clickhouse under Managed Postgres → Configure → Extensions and removed it from Integrations → Data integrations. Files remain physically at integrations/connectors/tools/pg_clickhouse/ so existing file-path URLs continue to work.
• Updated the frontmatter slug: field on the three pg_clickhouse pages to the new /cloud/managed-postgres/extensions/pg_clickhouse[/tutorial,/reference] slugs so the Docusaurus↔Mintlify slug map stays in sync.
• Updated cross-references in extensions.mdx and quickstart.mdx to point at the pg_clickhouse intro page.
• Added redirects in _site/redirects.json for the three old /integrations/pg_clickhouse[...] URLs.

Ambiguities / divergences from upstream

• BetaBadge vs PrivatePreviewBadge: upstream uses <BetaBadge link=... galaxyTrack galaxyEvent="docs.managed-postgres.migration-overview-beta" />, but the Mintlify BetaBadge snippet here doesn't accept those props yet and the sibling migration pages still use <PrivatePreviewBadge .../>. I matched the local convention (PrivatePreviewBadge with slug="migration-overview"). A follow-up may want to port the full BetaBadge replacement (upstream PR #6259) and switch this page over.
• ClickPipes page: upstream sidebar references cloud/managed-postgres/migrations/clickpipes, but the Mintlify equivalent is still products/managed-postgres/migrations/clickhouse-cloud.mdx. The overview page and the new sidebar both point at clickhouse-cloud, and the upstream clickhouse-cloud → clickpipes redirect already exists.
• Migrations FAQ: upstream introduces a migrations/faq page and links to it from the overview; no Mintlify equivalent exists, so that link is omitted from the overview here.
• PR template fix (.github/pull_request_template.md) and the vercel.json changes from the source PR are Docusaurus-side concerns and have no Mintlify counterpart; the equivalent redirect entries were added to _site/redirects.json instead.

Context

Triggered by merge to restructure-managed-postgres-sidebar on clickhouse-docs (commit 2a49607).

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Note

Low Risk
Documentation-only changes (navigation, new overview page, slug updates, redirects); no application or security logic.

Overview
Reorganizes Managed Postgres docs into four sidebar groups (Get started, Use it, Configure, Operate & reference) and adds a new Data migration overview that compares ClickPipes, PeerDB, pg_dump/pg_restore, and logical replication.

pg_clickhouse moves in the nav from Integrations → Data integrations to Configure → Extensions (files stay under integrations/connectors/tools/pg_clickhouse/). Frontmatter slug values on the intro, tutorial, and reference pages switch to /cloud/managed-postgres/extensions/pg_clickhouse[...], with matching entries in _site/redirects.json from the old /integrations/pg_clickhouse URLs. Integrations navigation.json drops the nested pg_clickhouse group; the three MDX pages get minor heading normalization and a small typo fix in reference.

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