feat(chat): floating side chat + shared resizable floating window

[Harry19081]

Summary

Adds a global floating side chat — a picture-in-picture chat window that floats over the whole pane surface (chat pane and stations) — and extracts the kanban session preview's floating-window mechanics into a shared FloatingWindow shell that now supports resizing. Both windows use the same shell, header, edge margins, and default height.

Problem

• There was no way to watch or drive a second session without leaving the active chat tab, and no way to start a new session in place while a station filled the view.
• The kanban session preview was the only floating window; its drag mechanics lived inside DetailPanelHeader, it couldn't be resized, and its clamps used the overlay's border box — so it could be dragged flush against (and effectively over) the pane edge.

Solution

Shared floating-window shell — src/components/FloatingWindow/

• useWindowDrag moved here (unchanged behavior); new useWindowResize with invisible edge/corner handles, min/max px caps.
• windowGeometry.ts keeps all geometry on the DOM element (dataset + inline style) so drag and resize can't drift and never re-render React. The first resize "pins" the window from fluid CSS to explicit absolute px geometry.
• Clamps (drag, resize, re-fit on host resize) use the overlay's content box, so the overlay's padding is a hard edge margin — 12px for both windows.
• DetailPanelHeader's draggable mode now also drops the bottom border; the kanban's one-off SCSS rule for this is removed. Both windows share one header.

Side chat — src/engines/ChatPanel/SideChat/

• Hosted by AppLayout over the pane surface (inside ChatProvider/SessionSyncProvider), so it works with the chat pane open, collapsed, or a station showing.
• Two modes via sideChatAtom: a session id → live transcript + composer; null → the chat pane's own injected session launcher (launchpad layout: agent hero + glowing composer, action cards hidden), adopting the new session in place after a background launch.
• Header actions: move to chat pane tab (reopens a collapsed pane) and new chat.
• Triggers: tab-strip + menu → Side Chat, and session tab right-click → Open in Side Chat. i18n keys added to all 13 locales.
• Deliberately does not reuse SessionContentView/ChatView: those claim the single global event pipeline, which would hijack the visible main chat. It renders like subagent grid cells instead (ChatSessionContext + per-session snapshot family) and sends via session-targeted SessionService.sendMessage. Documented in the component header.

Kanban preview: now resizable via the shared shell, with the same 12px margin, borderless header, and 600px default height. No changes to TaskDetailPanel.

Potential risks

• Kanban preview behavior change: gains resize handles (5px invisible edge strips inside the surface) and a slightly larger edge margin (8/8/4 → 12px). Drag behavior is otherwise identical.
• DetailPanelHeader draggable now implies borderless — the only current draggable callers are the two floating windows, so docked panels are unaffected.
• Side chat composer is lightweight: plain sendMessage (user_submit) with no model/mode pills or attachments; it does not run the main composer's resume/interrupt orchestration, so it's best suited to running or recently idle sessions.
• Side chat is single-instance (one window app-wide); opening a second session replaces the first.

Validation / Test plan

• pnpm typecheck: 0 errors in changed files (staged set typechecks cleanly in isolation on top of develop).
• pnpm vitest run src/features/TaskKanban src/engines/ChatPanel src/modules/shared: 206 files / 1363 tests pass, incl. an updated ChatPanelTabBar plus-menu test.
• eslint clean on all changed files; pre-commit lint-staged + scoped typecheck passed.
• Manual: open side chat from + menu → launcher shows agent name only (no cards); launch → window switches to the session; drag/resize can't cross the 12px margin; move-to-tab reopens a collapsed pane; kanban preview resizes from any edge/corner.