Split Cloud API client operations and conversions by domain

[sdairs]

Parent: #317

Stack position: 2 of 7. Starts after the analyzer module-tree change.

Goal

Split the non-model portions of clickhouse-cloud-api by product domain while preserving every public method, conversion, and crate-root export.

Scope

• Keep client.rs as a facade containing Client, authentication, constructors, shared HTTP helpers, and Query API helpers.
• Move OpenAPI operation methods into private domain modules for organizations, API keys, services, backups, Postgres, ClickPipes, ClickStack, activity, and UDFs.
• Keep convert.rs as a facade containing MissingRequiredFields and re-exports.
• Move ClickStack, Postgres, service, and shared write-back conversions into private domain modules.
• Preserve existing public paths through facade re-exports; do not expose the domain modules themselves.

Acceptance

• All existing Client method names, signatures, and behavior are unchanged.
• MissingRequiredFields and all From/TryFrom implementations remain available at their existing paths.
• The analyzer inventories the same OpenAPI operation set after the move.
• Existing client, query, conversion, and model tests pass unchanged in behavior.
• cargo check --workspace --all-features, focused tests, clippy, and rustfmt pass.

Out of scope

• Moving declarations out of models.rs.
• Renaming methods or models, changing request/response shapes, or adding API operations.