docs: port Managed Postgres pricing page with BetaBadge tracking

[mintlify]

Summary

Ports ClickHouse/clickhouse-docs#6284 (Wire BetaBadge tracking and drop inaccurate fallback disclaimer on Postgres pricing).

Changes

• Add products/managed-postgres/pricing.mdx — the Docusaurus pricing page (introduced in upstream #6282) had not yet been ported to Mintlify, so this PR brings the page over in its post-#6284 state.
• Wire the BetaBadge with link="https://clickhouse.com/cloud/postgres", galaxyTrack={true}, and galaxyEvent="docs.managed-postgres.pricing-beta" per the source PR.
• Omit the instance-fallback disclaimer bullet (the change made by #6284).
• Add pricing to the Managed Postgres navigation.json under "Get started", matching the source sidebar order (after quickstart).
• Extend snippets/components/BetaBadge/BetaBadge.jsx to support link, galaxyTrack, and galaxyEvent props (mirrors the source src/theme/badges/BetaBadge), so the badge renders as a tracked external link via galaxyOnClick.

Mintlify transforms applied

• .md → .mdx; sidebar_label → sidebarTitle.
• BetaBadge import path switched from @theme/badges/BetaBadge to the local snippet component.
• :::tip[Pricing calculator] admonition converted to <Tip>.
• The Docusaurus inline-styled tier-cards grid (which relied on var(--ifm-*) CSS variables) was converted to a Mintlify <CardGroup cols={3}> with <Card>s.
• Internal links rewritten from Docusaurus slugs to Mintlify file paths:
  • /cloud/manage/cloud-tiers → /products/cloud/features/cloud-tiers
  • /cloud/security/manage-my-account → /products/cloud/guides/security/cloud-access-management/manage-my-account
  • /cloud/infrastructure/clickhouse-private → /products/cloud/guides/infrastructure/deployment-options/clickhouse-private
  • In-product links to other managed-postgres pages rewritten from /docs/cloud/managed-postgres/* to /products/managed-postgres/* (the convention used elsewhere in this repo).
• Frontmatter slug left unchanged per migration mapping policy.

Ambiguities / notes

• The pricing page itself was introduced upstream in #6282 and had not been ported here yet. This PR ports the file in its current upstream state. If a separate port of #6282 is preferred, the disclaimer bullet would need to be re-added there and removed again here.
• The BetaBadge component previously ignored extra props; extending it to support link/galaxyTrack/galaxyEvent is a small behavioral change. The non-link variant is unchanged.
• Galaxy tracking depends on window.galaxy being available at runtime; in local preview it no-ops via the existing galaxyOnClick shim.

Validation

• mint validate ✅
• mint broken-links ✅ (no new broken links from this PR; remaining 2 in integrations/language-clients/java/jdbc.mdx are pre-existing and unrelated)

---

Note

Low Risk
Documentation and presentational component changes only; pricing copy omits one disclaimer bullet, which is a minor accuracy/navigation note for readers.

Overview
Adds the Managed Postgres pricing reference page to Mintlify and surfaces it in the sidebar under Get started (after quickstart). The page uses a tracked Beta badge linking to Cloud Postgres, Mintlify CardGroup tier comparison, and Mintlify path/slug conventions; it drops the upstream disclaimer about billing when a comparable instance is substituted during shortages.

BetaBadge now optionally renders as an external link with Galaxy click tracking (link, galaxyTrack, galaxyEvent); the default in-page “Beta feature” badge is unchanged.

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Project	Status	Preview	Updated (UTC)
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[cursor]

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

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^{Reviewed by Cursor Bugbot for commit fc0b06c. Configure here.}

[cursor]

Duplicate pricing in navigation

Medium Severity

This commit adds products/managed-postgres/pricing under Get started, but the same page path is already listed under the Pricing group, so the pricing doc can appear twice in the Managed Postgres sidebar.

Additional Locations (1)

• products/managed-postgres/navigation.json#L36-L37

 

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