Update query API endpoints docs

[Blargian]

Summary

Updates the query API endpoints docs to address #4054

• Adds examples for both GET in addition to POST
• Updates screenshots
• various other formatting improvements

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/docusaurus.config.js
• 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

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Project	Deployment	Preview	Updated (UTC)
clickhouse-docs	Ready	Preview	Sep 29, 2025 7:24pm

[Blargian]

Preview link: https://clickhouse-docs-gh688kwj2-clickhouse.vercel.app/docs/cloud/get-started/query-endpoints

[Blargian]

@ArctypeZach could I please ask for a review if you have a chance?