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/pipeline/indexing.pipeline.ts

@@ -187,20 +187,28 @@ export class IndexingPipeline {
 			this.replaceSnippets(repo.id, changedDocIds, newDocuments, newSnippets);
 
 			// ---- Stage 4: Embeddings (if provider is configured) ----------------
-			if (this.embeddingService && newSnippets.length > 0) {
-				const snippetIds = newSnippets.map((s) => s.id!);
+			if (this.embeddingService) {
+				const snippetIds = this.embeddingService.findSnippetIdsMissingEmbeddings(
+					repo.id,
+					normJob.versionId
+				);
+
+				if (snippetIds.length === 0) {
+					// No missing embeddings for the active profile; parsing progress is final.
+				} else {
 				const embeddingsTotal = snippetIds.length;
 
-				await this.embeddingService.embedSnippets(snippetIds, (done) => {
-					const progress = calculateProgress(
-						processedFiles,
-						totalFiles,
-						done,
-						embeddingsTotal,
-						true
-					);
-					this.updateJob(job.id, { progress });
-				});
+					await this.embeddingService.embedSnippets(snippetIds, (done) => {
+						const progress = calculateProgress(
+							processedFiles,
+							totalFiles,
+							done,
+							embeddingsTotal,
+							true
+						);
+						this.updateJob(job.id, { progress });
+					});
+				}
 			}
 
 			// ---- Stage 5: Update repository stats --------------------------------