fix(client): share the side-card width across sessions (last drag wins)

[fsvov]

Problem

The side-card panel width is stored in the per-session state (dsh-sidebar:v1:<sessionId> in localStorage). Dragging the panel in one conversation writes only that session's width — switching to another conversation snaps the panel back to that session's own width (its persisted value or the "default width share" seed). The width is a layout preference, not session content, so per-session isolation here is surprising: users expect the width they chose to hold across conversations.

Fix

Make the panel width a cross-session preference with "last drag wins":

• New global key dsh-sidebar:v1:width (next to the per-session keys).
• schedulePersist writes the current width to the global key on every persist (any width change — drag or fullscreen toggle — becomes the shared width).
• loadState prefers the global width over a session's persisted value, and the fresh-session seed uses it too.
• A cache-hit session switch (setSession) adopts the global width, so already-loaded sessions stay in sync within the same page lifetime.

Everything else (open/closed state, tabs, splits, bottom-panel height) stays per-session, exactly as before.

Backward compatibility

With no global key present (first run after upgrade, or pre-existing sessions), the behavior is byte-for-byte unchanged: readGlobalWidth() returns undefined and every code path falls through to the original logic. The first drag anywhere seeds the global key; from then on all conversations follow it.

Tests

Added a regression test in tests/unit.spec.ts ("shares the panel width across sessions (last drag wins)") that drives the real store with a storage-backed localStorage stub:

1. drag in session A → 500;
2. switch to fresh session B → width is 500 (was the default 400 before this change);
3. drag in B → 600, switch back to cached A → width is 600.

tests/service.spec.ts and the store suites pass; the two unit.spec.ts failures (requireAbsolute POSIX-path expectation and defaultShell expecting /bin/bash) are pre-existing Windows-platform issues, reproduced identically without this change.

Design note

An alternative would be a settings toggle ("sync width across conversations") backed by the existing side-card prefs document — happy to rework toward that if the maintainers prefer an opt-in pref over the unconditional behavior. The panel width has no session-specific meaning today (it is a pure viewport preference), which is why this change makes it global unconditionally.