Remove Managed Postgres benchmarks page and link to blog post

[yashpreetbathla]

Summary

The standalone benchmarks page is removed in favor of pointing readers
to the blog post at clickhouse.com/blog/postgresbench.

• Deletes benchmarks.md and removes it from the sidebar
• Replaces the inline benchmarks link in the overview with a note
  pointing to the blog post

Checklist

• Delete items not relevant to your PR
• URL changes should add a redirect to the old URL via https://github.com/ClickHouse/clickhouse-docs/blob/main/vercel.json
• If adding a new integration page, also add an entry to the integrations list here: https://github.com/ClickHouse/clickhouse-docs/blob/main/docs/integrations/index.mdx

---

Note

Low Risk
Documentation-only navigation and copy changes; main follow-up is a possible redirect for the removed doc URL.

Overview
Removes the in-docs Managed Postgres performance benchmarks page and routes readers to the external blog post at clickhouse.com/blog/postgresbench instead.

benchmarks.md is deleted and cloud/managed-postgres/benchmarks is dropped from the Managed Postgres sidebar in sidebars.js. On overview.md, the internal link to the benchmarks doc is replaced with a short note linking to that blog post. The NVMe bullet is also reworded from unlimited local IOPS to 10x sustained IOPS limits (with the existing footnote).

Consider adding a vercel.json redirect for the old /cloud/managed-postgres/benchmarks URL if it was published; localized i18n/*/benchmarks.md copies may still exist outside this diff.

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[vercel]

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Project	Deployment	Actions	Updated (UTC)
clickhouse-docs	Ready	Preview, Comment	May 27, 2026 11:10pm

4 Skipped Deployments

Project	Deployment	Actions	Updated (UTC)
clickhouse-docs-jp	Ignored		May 27, 2026 11:10pm
clickhouse-docs-ko	Ignored		May 27, 2026 11:10pm
clickhouse-docs-ru	Ignored		May 27, 2026 11:10pm
clickhouse-docs-zh	Ignored		May 27, 2026 11:10pm

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[mintlify]

Docs PR opened: ClickHouse/mintlify-docs-dev#88

Removed the Managed Postgres benchmarks page and added a note in the overview linking to the benchmarks blog post.