The panel width lived in the per-session state (dsh-sidebar:v1:<id>), so a
drag in one conversation never carried to another: switching conversations
snapped the panel back to that session's own width. The width is a layout
preference, not session content, so it now persists under a cross-session
key (dsh-sidebar:v1:width):
- every persist writes the current width to the global key;
- loadState prefers the global width over a session's persisted one;
- a cache-hit session switch adopts the global width.
Backward compatible: with no global key present (first run / older data)
the behavior is unchanged. Adds a regression test covering drag-in-A ->
switch-to-B and drag-in-B -> switch-back-to-A.