fix(popover): gate visibility until positioned, tighten types

src/shared/ui/Popover/Popover.svelte

@@ -47,7 +47,7 @@ interface Props {
      * ARIA role for the content
      * @default 'dialog'
      */
-    role?: string;
+    role?: 'dialog' | 'menu' | 'listbox';
     /**
      * Trigger snippet — spread the provided props onto your trigger element
      */
@@ -74,8 +74,20 @@ const contentId = `popover-${uid}`;
 
 let triggerEl: HTMLElement | undefined = $state();
 let contentEl: HTMLElement | undefined = $state();
+/**
+ * Side actually used after flip. Seeded from the `side` prop; the authoritative
+ * value is written by updatePosition() on every open, so the seed only matters
+ * for the closed state (hence the intentional state_referenced_locally warning).
+ */
 let resolvedSide = $state(side);
 
+/**
+ * True once updatePosition has applied coordinates for the current open.
+ * Gates visibility so the content never paints at its pre-positioned (0,0)
+ * top-layer default before the first measurement.
+ */
+let positioned = $state(false);
+
 /**
  * Actual DOM open state, driven by the `toggle` event. Source of truth for
  * whether the browser currently shows the popover; `open` is the public binding.
@@ -122,14 +134,18 @@ function updatePosition(): void {
     resolvedSide = result.side;
     contentEl.style.left = `${result.x}px`;
     contentEl.style.top = `${result.y}px`;
+    positioned = true;
 }
 
 /**
  * Mirror the `toggle` event into our state.
  */
-function onToggle(event: Event & { newState?: string }): void {
+function onToggle(event: ToggleEvent): void {
     shown = event.newState === 'open';
     open = shown;
+    if (!shown) {
+        positioned = false;
+    }
 }
 
 /**
@@ -175,6 +191,11 @@ $effect(() => {
 
 {@render trigger(triggerProps)}
 
+<!--
+    inset:auto + margin:0 neutralize the UA popover stylesheet (which sets
+    inset:0; margin:auto to center it) so the JS-applied left/top win.
+    visibility is hidden until updatePosition runs (see `positioned`).
+-->
 <div
     bind:this={contentEl}
     id={contentId}
@@ -183,7 +204,7 @@ $effect(() => {
     data-side={resolvedSide}
     data-state={shown ? 'open' : 'closed'}
     ontoggle={onToggle}
-    style="position: fixed; inset: auto; margin: 0;"
+    style={`position: fixed; inset: auto; margin: 0;${positioned ? '' : ' visibility: hidden;'}`}
     class={cn(
         'opacity-0 scale-95 transition-discrete transition-all duration-fast',
         'starting:opacity-0 starting:scale-95',