Streamline thread start handler

[pakrym-oai]

Why

The thread start handler mixed request validation, thread construction, dynamic-tool validation, and JSON-RPC error emission in one nested flow. Returning request errors from the helper path makes the successful setup path easier to follow.

What Changed

• Reworked thread/start handling in codex-rs/app-server/src/codex_message_processor.rs so helper methods return Result and the handler emits one result.
• Moved dynamic-tool validation failures into returned JSON-RPC errors instead of local send_error branches.
• Preserved the existing thread creation and task-spawning behavior.

Verification

• cargo check -p codex-app-server
• cargo test -p codex-app-server --test all v2::dynamic_tools -- --test-threads=1
• cargo test -p codex-app-server --test all v2::turn_start -- --test-threads=1