feat(#81): improve discussion discoverability

- Add comment count badge on the Discussion tab (seeded from SSR, updated live)
- Add 'Diskussion starten' nudge above collapsed panel when no comments exist
- Add empty state hint with speech-bubble icon inside the discussion panel
- Fix CommentThread to fire onCountChange with SSR-seeded count on mount
- Add tests for all three behaviours in CommentThread and DocumentBottomPanel

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

frontend/src/lib/components/DocumentBottomPanel.svelte

@@ -98,10 +98,16 @@ const tabs: { id: DocumentPanelTab; label: () => string }[] = [
 ];
 
 const panelHeight = $derived(open ? height : MIN_HEIGHT);
+
+let discussionCount = $state((() => comments.reduce((s, c) => s + 1 + c.replies.length, 0))());
+
+function handleCountChange(count: number) {
+	discussionCount = count;
+}
 </script>
 
 <div
-	class="fixed right-0 bottom-0 left-0 z-30 flex flex-col border-t border-line bg-surface shadow-[0_-4px_16px_rgba(0,0,0,0.08)]"
+	class="fixed relative right-0 bottom-0 left-0 z-30 flex flex-col border-t border-line bg-surface shadow-[0_-4px_16px_rgba(0,0,0,0.08)]"
 	style="height: {panelHeight}px"
 	data-testid="bottom-panel"
 >
@@ -120,6 +126,15 @@ const panelHeight = $derived(open ? height : MIN_HEIGHT);
 		<div class="h-1 w-12 rounded-full bg-line"></div>
 	</div>
 
+	{#if !open && discussionCount === 0}
+		<button
+			data-testid="discussion-nudge"
+			onclick={() => openTab('discussion')}
+			class="absolute -top-7 left-1/2 -translate-x-1/2 rounded-full border border-line bg-surface px-3 py-1 font-sans text-xs whitespace-nowrap text-ink-3 shadow-sm transition-colors hover:text-ink"
+			>{m.comment_start_discussion()}</button
+		>
+	{/if}
+
 	<!-- Tab bar -->
 	<div class="flex shrink-0 items-center border-b border-line bg-surface px-4">
 		{#each tabs as tab (tab.id)}
@@ -131,6 +146,13 @@ const panelHeight = $derived(open ? height : MIN_HEIGHT);
 				aria-pressed={activeTab === tab.id && open}
 			>
 				{tab.label()}
+				{#if tab.id === 'discussion' && discussionCount > 0}
+					<span
+						data-testid="discussion-count-badge"
+						class="ml-1.5 inline-flex h-4 min-w-4 items-center justify-center rounded-full bg-primary px-1 font-sans text-[10px] font-bold text-white"
+						>{discussionCount}</span
+					>
+				{/if}
 			</button>
 		{/each}
 
@@ -165,6 +187,7 @@ const panelHeight = $derived(open ? height : MIN_HEIGHT);
 					canComment={canComment}
 					currentUserId={currentUserId}
 					canAdmin={canAdmin}
+					onCountChange={handleCountChange}
 				/>
 			{:else if activeTab === 'history'}
 				<PanelHistory documentId={doc.id} />