Extract auth, activity, backup, and API-key CLI domains

[sdairs]

Closes #384

Summary

• Co-locate auth clap definitions and dispatch with cloud authentication.
• Extract activity, backup/backup-config, and API-key vertical slices, including clap, dispatch, handlers, builders, client wrappers, output, and tests.
• Preserve service backup-config classification and shared API-key cleanup/provisioning workflows.
• Remove the moved handlers and wrappers from generic cloud monoliths without changing commands, requests, or output.

Tests

• cargo fmt --all
• cargo check --workspace --all-features
• cargo test -p clickhousectl
• cargo clippy -p clickhousectl --all-targets -- -D warnings

[Copilot]

Pull request overview

This PR refactors the clickhousectl cloud CLI by extracting the auth, activity, backups (including backup-config), and API-key domains into dedicated vertical-slice modules, while keeping the public CLI surface and behavior stable via re-exports through cloud::cli.

Changes:

• Move auth clap definitions + dispatch/handlers into cloud::auth, and route cloud auth ... through auth::run.
• Extract activity, backups/backup-config, and API-key command stacks (clap types, dispatch, handlers, request builders, CloudClient wrappers, and tests) into cloud::activity, cloud::backups, and cloud::api_keys.
• Remove the corresponding handlers/wrappers from cloud::commands / cloud::client, and update call sites to use the extracted modules (including shared API-key cleanup/provisioning helpers).

Reviewed changes

Copilot reviewed 9 out of 9 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
crates/clickhousectl/src/cloud/service_query.rs	Switches provisioning cleanup to use the shared api_keys::discard_api_key helper.
crates/clickhousectl/src/cloud/mod.rs	Adds new domain modules and delegates auth/activity/backup/key dispatch into them.
crates/clickhousectl/src/cloud/commands.rs	Removes extracted handlers/builders and imports shared API-key cleanup helpers for service deletion.
crates/clickhousectl/src/cloud/client.rs	Removes activity/backup/backup-config/api-key wrapper methods now owned by the extracted modules.
crates/clickhousectl/src/cloud/cli.rs	Re-exports extracted clap enums and delegates write-classification to per-domain is_write() methods.
crates/clickhousectl/src/cloud/backups.rs	New backups + backup-config domain slice (clap, handlers, request builder, CloudClient wrappers, tests).
crates/clickhousectl/src/cloud/auth.rs	Co-locates auth clap definitions and handlers; adds tests for parsing and write classification.
crates/clickhousectl/src/cloud/api_keys.rs	New API-key domain slice including builders, cleanup helpers, CloudClient wrappers, and tests.
crates/clickhousectl/src/cloud/activity.rs	New activity domain slice (clap, handlers, CloudClient wrappers, tests).

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[iskakaushik]

LGTM