test(api): add full-admin HTTP tests for registered_clients mutations

[sergey3bv]

Summary

• Extends tests with POST/PATCH/DELETE success paths under full admin;
• Adds helpers and DB cleanup.

Avoid naming corporate partners, customers, or other sensitive external brands in this PR title or body. Use generic descriptors unless a maintainer explicitly approves the public reference.

Motivation

• A follow-up for test(admin): add negative HTTP-layer tests for registered_clients full-admin gate #175

Related Issue

• Closes Follow-up: add positive full-admin create/update/delete HTTP tests for registered_clients #182

Testing

• cargo test --workspace --verbose
• cargo clippy --workspace --all-targets --all-features -- -D warnings -A deprecated
• cargo fmt --all -- --check
• Manual verification completed

Visuals

• UI/web change with screenshots/video attached
• No visual change
• Visuals and text avoid sensitive external brand or partner names unless explicitly approved