Fix docked-panel expand and history-drag regressions

Two issues Ahmed flagged on the chat-dock PR. First, the right-side
history panel's drag-resize broke once a second right-side FlexPanel
mounted -- DraggableSeparator's cached useElementBounding only refreshes
on size/scroll changes, not when a sibling shifts our position. Calling
update() on each drag tick keeps the math honest. Second, the chat
dock's collapse chevron was setting only FlexPanel's local show ref
while chatStore.chatVisible stayed true, so the activity-bar icon
needed two clicks to bring the panel back. FlexPanel now emits a close
event the chat parent maps to chatStore.hideChat() (history panel
keeps its existing local-state fallback). Also marks the route watcher
as immediate so a direct hit on /chatgxy doesn't double up with the
dock at hydration.

Author: dannon

client/src/components/Common/DraggableSeparator.vue

@@ -41,6 +41,11 @@ onMounted(() => {
 });
 
 const rootBoundingBox = useElementBounding(positionedParent);
+// useElementBounding only refreshes on size/scroll changes, not when a sibling
+// mounts/unmounts and shifts our position. Re-measure on each drag tick so the
+// math survives layout reflows triggered elsewhere (e.g. a second right-side
+// FlexPanel appearing or disappearing).
+const refreshBoundingBox = rootBoundingBox.update;
 
 const { position: draggablePosition, isDragging } = useDraggable(draggable, {
     preventDefault: true,
@@ -66,6 +71,7 @@ watch(
 const borderWidth = 6;
 
 function updatePosition() {
+    refreshBoundingBox();
     if (props.side === "left") {
         handlePosition.value = draggablePosition.value.x - rootBoundingBox.left.value + borderWidth;
     } else {

client/src/components/Panels/FlexPanel.vue

@@ -26,6 +26,7 @@ const props = withDefaults(defineProps<Props>(), {
 
 const emit = defineEmits<{
     (e: "update:reactive-width", width: number): void;
+    (e: "close"): void;
 }>();
 
 const localPanelWidth = ref(DEFAULT_WIDTH);
@@ -109,7 +110,10 @@ defineExpose({
             class="collapse-button open"
             :class="{ ...sideClasses, show: showToggle }"
             title="Close panel"
-            @click="show = false"
+            @click="
+                show = false;
+                emit('close');
+            "
             @mouseenter="hoverToggle = true"
             @focusin="hoverToggle = true"
             @mouseout="hoverToggle = false"

client/src/entry/analysis/modules/Analysis.vue

@@ -32,6 +32,7 @@ watch(
             chatStore.hideChat();
         }
     },
+    { immediate: true },
 );
 
 const showCenter = ref(false);
@@ -100,7 +101,8 @@ onUnmounted(() => {
             v-if="showPanels && isRightPanelOpen"
             panel-id="chat-panel"
             side="right"
-            :reactive-width.sync="chatPanelWidth">
+            :reactive-width.sync="chatPanelWidth"
+            @close="chatStore.hideChat()">
             <ChatGXY
                 :exchange-id="activeChatId || undefined"
                 docked