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.ts

@@ -23,6 +23,42 @@ export class EmbeddingService {
 		private readonly profileId: string = 'local-default'
 	) {}
 
+	findSnippetIdsMissingEmbeddings(repositoryId: string, versionId: string | null): string[] {
+		if (versionId) {
+			const rows = this.db
+				.prepare<[string, string, string], { id: string }>(
+					`SELECT snippets.id
+					 FROM snippets
+					 LEFT JOIN snippet_embeddings
+					   ON snippet_embeddings.snippet_id = snippets.id
+					  AND snippet_embeddings.profile_id = ?
+					 WHERE snippets.repository_id = ?
+					   AND snippets.version_id = ?
+					   AND snippet_embeddings.snippet_id IS NULL
+					 ORDER BY snippets.id`
+				)
+				.all(this.profileId, repositoryId, versionId);
+
+			return rows.map((row) => row.id);
+		}
+
+		const rows = this.db
+			.prepare<[string, string], { id: string }>(
+				`SELECT snippets.id
+				 FROM snippets
+				 LEFT JOIN snippet_embeddings
+				   ON snippet_embeddings.snippet_id = snippets.id
+				  AND snippet_embeddings.profile_id = ?
+				 WHERE snippets.repository_id = ?
+				   AND snippets.version_id IS NULL
+				   AND snippet_embeddings.snippet_id IS NULL
+				 ORDER BY snippets.id`
+			)
+			.all(this.profileId, repositoryId);
+
+		return rows.map((row) => row.id);
+	}
+
 	/**
 	 * Embed the given snippet IDs and store the results in snippet_embeddings.
 	 *