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 a small optional BetaBadge UI/tracking extension only; no application runtime or security logic changes.

Overview
Adds a Managed Postgres pricing reference page to Mintlify and surfaces it in the Get started nav (after quickstart).

The new pricing.mdx documents NVMe-based VM pricing, tier limits (Basic / Scale / Enterprise via <CardGroup>), instance families, beta terms (free until June 15, 2026, 50% discount), calculator usage, and GA disclaimers—without the upstream instance-fallback disclaimer bullet removed in source #6284. The page uses a BetaBadge that links to Cloud Postgres with Galaxy click tracking (docs.managed-postgres.pricing-beta).

BetaBadge.jsx now accepts optional link, galaxyTrack, and galaxyEvent: when link is set, the badge renders as an external anchor with optional galaxyOnClick tracking; the default in-page “Learn more” badge is unchanged.

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Project	Status	Preview	Updated (UTC)
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