feat(EMBEDDINGS-0001): enable local embedder by default and overhaul settings page

- Wire local embedding provider as the default on startup when no profile is configured
- Refactor embedding settings into dedicated service, DTOs, mappers and models
- Rebuild settings page with profile management UI and live test feedback
- Expose index summary (indexed versions + embedding count) on repo endpoints
- Harden indexing pipeline and context search with additional test coverage

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

src/lib/server/embeddings/embedding.service.test.ts

@@ -408,6 +408,36 @@ describe('EmbeddingService', () => {
 		expect(embedding![2]).toBeCloseTo(0.2, 5);
 	});
 
+	it('stores embeddings under the configured profile ID', async () => {
+		client
+			.prepare(
+				`INSERT INTO embedding_profiles
+				 (id, provider_kind, title, enabled, is_default, model, dimensions, config, created_at, updated_at)
+				 VALUES (?, ?, ?, ?, ?, ?, ?, ?, unixepoch(), unixepoch())`
+			)
+			.run(
+				'openai-custom',
+				'openai-compatible',
+				'OpenAI Custom',
+				1,
+				0,
+				'test-model',
+				4,
+				'{}'
+			);
+
+		const snippetId = seedSnippet(db, client);
+		const provider = makeProvider(4, 'test-model');
+		const service = new EmbeddingService(client, provider, 'openai-custom');
+
+		await service.embedSnippets([snippetId]);
+
+		const row = client
+			.prepare('SELECT profile_id FROM snippet_embeddings WHERE snippet_id = ?')
+			.get(snippetId) as { profile_id: string };
+		expect(row.profile_id).toBe('openai-custom');
+	});
+
 	it('is idempotent — re-embedding replaces the existing row', async () => {
 		const snippetId = seedSnippet(db, client);
 		const provider = makeProvider(2);
@@ -469,6 +499,19 @@ describe('EmbeddingService', () => {
 		};
 		expect(rows.cnt).toBe(0);
 	});
+
+	it('finds snippets missing embeddings for the active profile', async () => {
+		const firstSnippetId = seedSnippet(db, client);
+		const secondSnippetId = seedSnippet(db, client, { content: 'Second snippet content' });
+		const provider = makeProvider(4);
+		const service = new EmbeddingService(client, provider, 'local-default');
+
+		await service.embedSnippets([firstSnippetId]);
+
+		expect(service.findSnippetIdsMissingEmbeddings('/test/embed-repo', null)).toEqual([
+			secondSnippetId
+		]);
+	});
 });
 
 // ---------------------------------------------------------------------------