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.spec.ts

@@ -0,0 +1,74 @@
+import { describe, it, expect, afterEach } from 'vitest';
+import { cleanup, render } from 'vitest-browser-svelte';
+import { page, userEvent } from 'vitest/browser';
+import DocumentBottomPanel from './DocumentBottomPanel.svelte';
+import type { Comment } from '$lib/types';
+
+afterEach(cleanup);
+
+function makeComment(id: string): Comment {
+	return {
+		id,
+		authorId: 'user-1',
+		authorName: 'Alice',
+		content: 'Hello',
+		createdAt: new Date().toISOString(),
+		updatedAt: new Date().toISOString(),
+		replies: []
+	};
+}
+
+const doc = { id: 'doc-1', title: 'Test' };
+
+const baseProps = {
+	doc,
+	canComment: true,
+	currentUserId: 'user-1',
+	canAdmin: false,
+	height: 300,
+	activeTab: 'discussion' as const
+};
+
+describe('DocumentBottomPanel – discussion badge', () => {
+	it('shows a badge with comment count on the Discussion tab when comments exist', async () => {
+		render(DocumentBottomPanel, {
+			...baseProps,
+			comments: [makeComment('c-1'), makeComment('c-2')],
+			open: true
+		});
+		await expect.element(page.getByTestId('discussion-count-badge')).toBeInTheDocument();
+		await expect.element(page.getByTestId('discussion-count-badge')).toHaveTextContent('2');
+	});
+
+	it('does not show badge when there are no comments', async () => {
+		render(DocumentBottomPanel, { ...baseProps, comments: [], open: true });
+		await expect.element(page.getByTestId('discussion-count-badge')).not.toBeInTheDocument();
+	});
+});
+
+describe('DocumentBottomPanel – start discussion nudge', () => {
+	it('shows nudge above drag handle when panel is closed and no comments', async () => {
+		render(DocumentBottomPanel, { ...baseProps, comments: [], open: false });
+		await expect.element(page.getByTestId('discussion-nudge')).toBeInTheDocument();
+	});
+
+	it('does not show nudge when panel is closed but comments exist', async () => {
+		render(DocumentBottomPanel, {
+			...baseProps,
+			comments: [makeComment('c-1')],
+			open: false
+		});
+		await expect.element(page.getByTestId('discussion-nudge')).not.toBeInTheDocument();
+	});
+
+	it('does not show nudge when panel is open', async () => {
+		render(DocumentBottomPanel, { ...baseProps, comments: [], open: true });
+		await expect.element(page.getByTestId('discussion-nudge')).not.toBeInTheDocument();
+	});
+
+	it('opens the discussion tab when the nudge is clicked', async () => {
+		render(DocumentBottomPanel, { ...baseProps, comments: [], open: false });
+		await userEvent.click(page.getByTestId('discussion-nudge'));
+		await expect.element(page.getByTestId('bottom-panel-content')).toBeInTheDocument();
+	});
+});