feat: RHS panel initial fetch, floating widget, session cleanup (#5)

Phase 1: Fix RHS panel to fetch existing sessions on mount
- Add initial API fetch in useAllStatusUpdates() hook
- Allow GET /sessions endpoint without shared secret auth
- RHS panel now shows sessions after page refresh

Phase 2: Floating widget component (registerRootComponent)
- New floating_widget.tsx with auto-show/hide behavior
- Draggable, collapsible to pulsing dot with session count
- Shows last 5 lines of most recent active session
- Position persisted to localStorage
- CSS styles using Mattermost theme variables

Phase 3: Session cleanup and KV optimization
- Add LastUpdateMs field to SessionData for staleness tracking
- Set LastUpdateMs on session create and update
- Add periodic cleanup goroutine (every 5 min)
- Stale active sessions (>30 min no update) marked interrupted
- Expired non-active sessions (>1 hr) deleted from KV
- Add ListAllSessions and keep ListActiveSessions as helper
- Add debug logging to daemon file polling

Closes #5

plugin/webapp/src/styles/live_status.css

@@ -305,3 +305,141 @@
   letter-spacing: 0.5px;
   color: var(--center-channel-color-48, rgba(0, 0, 0, 0.48));
 }
+
+/* ========= Floating Widget Styles ========= */
+
+.ls-widget-collapsed {
+  position: fixed;
+  z-index: 9999;
+  cursor: pointer;
+  display: flex;
+  align-items: center;
+  gap: 4px;
+  padding: 8px;
+  background: var(--center-channel-bg, #fff);
+  border: 1px solid var(--center-channel-color-16, rgba(0, 0, 0, 0.16));
+  border-radius: 50%;
+  box-shadow: 0 2px 8px rgba(0, 0, 0, 0.15);
+  transition: transform 0.2s;
+}
+
+.ls-widget-collapsed:hover {
+  transform: scale(1.1);
+}
+
+.ls-widget-collapsed .ls-live-dot {
+  width: 12px;
+  height: 12px;
+}
+
+.ls-widget-count {
+  position: absolute;
+  top: -4px;
+  right: -4px;
+  background: #f44336;
+  color: #fff;
+  font-size: 10px;
+  font-weight: 700;
+  width: 16px;
+  height: 16px;
+  border-radius: 50%;
+  display: flex;
+  align-items: center;
+  justify-content: center;
+}
+
+.ls-widget-expanded {
+  position: fixed;
+  z-index: 9999;
+  width: 320px;
+  max-height: 300px;
+  background: var(--center-channel-bg, #fff);
+  border: 1px solid var(--center-channel-color-16, rgba(0, 0, 0, 0.16));
+  border-radius: 8px;
+  box-shadow: 0 4px 16px rgba(0, 0, 0, 0.15);
+  display: flex;
+  flex-direction: column;
+  overflow: hidden;
+  font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
+}
+
+.ls-widget-header {
+  display: flex;
+  align-items: center;
+  padding: 8px 10px;
+  background: var(--center-channel-color-04, rgba(0, 0, 0, 0.04));
+  border-bottom: 1px solid var(--center-channel-color-08, rgba(0, 0, 0, 0.08));
+  cursor: grab;
+  user-select: none;
+}
+
+.ls-widget-header:active {
+  cursor: grabbing;
+}
+
+.ls-widget-title {
+  display: flex;
+  align-items: center;
+  gap: 6px;
+  font-size: 12px;
+  font-weight: 600;
+  flex: 1;
+}
+
+.ls-widget-collapse-btn,
+.ls-widget-close-btn {
+  background: none;
+  border: none;
+  cursor: pointer;
+  font-size: 14px;
+  color: var(--center-channel-color-56, rgba(0, 0, 0, 0.56));
+  padding: 2px 6px;
+  border-radius: 3px;
+}
+
+.ls-widget-collapse-btn:hover,
+.ls-widget-close-btn:hover {
+  background: var(--center-channel-color-08, rgba(0, 0, 0, 0.08));
+}
+
+.ls-widget-body {
+  padding: 8px;
+  overflow-y: auto;
+  flex: 1;
+}
+
+.ls-widget-session {
+  margin-bottom: 4px;
+}
+
+.ls-widget-session-header {
+  display: flex;
+  align-items: center;
+  gap: 6px;
+  margin-bottom: 6px;
+}
+
+.ls-widget-lines {
+  font-family: 'SFMono-Regular', Consolas, 'Liberation Mono', Menlo, monospace;
+  font-size: 11px;
+  line-height: 1.5;
+  background: var(--center-channel-color-04, rgba(0, 0, 0, 0.04));
+  border-radius: 4px;
+  padding: 6px 8px;
+  max-height: 150px;
+  overflow-y: auto;
+}
+
+.ls-widget-empty {
+  color: var(--center-channel-color-48, rgba(0, 0, 0, 0.48));
+  font-size: 12px;
+  text-align: center;
+  padding: 12px;
+}
+
+.ls-widget-more {
+  font-size: 11px;
+  color: var(--center-channel-color-48, rgba(0, 0, 0, 0.48));
+  text-align: center;
+  padding: 4px;
+}