refactor(web-ui): split ui.ts orchestration into status, messages, runtime, and history modules

[lidge-jun]

Summary

public/js/ui.ts still mixes status badge control, system messages, process-block updates, streaming finalize, history bootstrap, and copy delegation in a single file.

Current Review Status

• Open after the 2026-04-18 pull audit
• public/js/ui.ts has grown to 656L
• The file still owns setStatus(), addSystemMsg(), showProcessStep(), finalizeAgent(), loadMessages(), and initMsgCopy() together

Suggested Scope

• Split the file into status, messages, process-runtime, and history modules while keeping the external API stable

Evidence

• public/js/ui.ts