Docs: own and sync ClickHouse documentation

[Blargian]

Summary

Make ClickHouse/clickhouse-c the source of truth for its public ClickHouse documentation.

• Copy the current C client documentation from ClickHouse/ClickHouse@21ed77718a5f454680497924d68e9f60a41e026c into docs/, with trailing whitespace normalized and a client-owned navigation.json.
• Add scoped Mintlify verification for the complete C documentation folder.
• Add a one-way sync workflow that replaces the corresponding folder in ClickHouse/ClickHouse after a release, manual dispatch, or merge carrying the sync-docs label.

The published URL remains unchanged. Folder ownership allows future pages to be reviewed alongside the client implementation and synchronized automatically.

Related: ClickHouse/ClickHouse#111223

After merge, maintainers should confirm the sync-docs label exists and the Workflow Auth GitHub App credentials are available to this repository.

Validation

• All workflows pass actionlint v1.7.7 and YAML parsing.
• navigation.json passes JSON parsing.
• git diff --check passes.
• The migrated folder matches the corresponding aggregator folder in Docs: organize language client docs into folders ClickHouse#111223.