docs: port managed-postgres branching and Supabase migration link

[mintlify]

Summary

Ports ClickHouse/clickhouse-docs#6347 — adds Managed Postgres branching (PITR) doc and a Supabase migration pointer.

Changes

• Add products/managed-postgres/branching.mdx (new PITR/branching guide).
• Add "Migrating from Supabase" section to products/managed-postgres/migrations/overview.mdx linking to the external migration gist.
• Insert branching after backup-and-restore in products/managed-postgres/navigation.json.

Context

• Source slugs preserved (/cloud/managed-postgres/branching, /cloud/managed-postgres/migrations/overview).
• Docusaurus BetaBadge swapped for the Mintlify snippet component.
• Internal links rewritten from /cloud/managed-postgres/... to /products/managed-postgres/... to match the convention used elsewhere in this repo.
• sidebars.js and styles/ClickHouse/Headings.yml from the source PR don't apply here (Mintlify uses navigation.json; there's no Vale config in this repo).

Ambiguity

The branching doc links to /cloud/managed-postgres/local-development, but docs/cloud/managed-postgres/local-development.md hasn't been ported to Mintlify yet. The link text is preserved as plain text with a TODO comment so it can be wired up once that page lands.

---

Note

Low Risk
Documentation and navigation only; no product code or security-sensitive behavior changes.

Overview
Adds a new Managed Postgres branching guide (branching.mdx) that documents PITR-based branches as independent deployments: how creation works, use cases, sizing, recovery time expectations, and guidance to prefer local dev over prod-derived branches for day-to-day work. The page uses the Mintlify BetaBadge snippet and links to backup/restore and local development under /products/managed-postgres/....

The migrations overview gains a Migrating from Supabase section pointing to an external step-by-step guide on GitHub. Navigation lists branching in Features immediately after backup-and-restore.

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[mintlify]

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[Blargian]

@copilot please resolve the TODO comment, i've merged the local-development changes, so you just need to merge main into this branch and update the TODO:

The branching doc links to /cloud/managed-postgres/local-development, but docs/cloud/managed-postgres/local- development.md hasn't been ported to Mintlify yet. The link text is preserved as plain text with a TODO comment so it can be wired up once that page lands.

[Copilot]

@copilot please resolve the TODO comment, i've merged the local-development changes, so you just need to merge main into this branch and update the TODO:

The branching doc links to /cloud/manage...

Done — merged main (which brought in products/managed-postgres/local-development.mdx) and replaced the plain-text + TODO comment with a live link: [Local development environments](/products/managed-postgres/local-development). See commit docs: resolve TODO - wire up local-development link in branching.mdx.

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