feat: migrate semantic search to pgvector + full-text search

Replace JSON-string embeddings with native pgvector(1536) storage and
add PostgreSQL full-text search (tsvector/GIN) with Reciprocal Rank Fusion
for hybrid keyword + semantic ranking.

Changes:
- NoteEmbedding.embedding: String → vector(1536) via pgvector
- NoteEmbedding: added updatedAt for reindex tracking
- Note: added tsv (tsvector) with auto-update trigger for FTS
- semantic-search.service: hybrid FTS + vector search with RRF fusion
- embedding.service: toVectorString() for pgvector SQL literals
- Removed JS-side cosine similarity loops (now DB-side via <=>)
- Added HNSW index on NoteEmbedding.embedding (cosine distance)
- Added GIN index on Note.tsv for FTS queries

Schema migration in: prisma/migrations/20260512120000_pgvector_and_fts_search/

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

memento-note/prisma/migrations/20260512120000_pgvector_and_fts_search/migration.sql

@@ -0,0 +1,52 @@
+-- Phase 1: Enable pgvector extension
+CREATE EXTENSION IF NOT EXISTS vector;
+
+-- Phase 2: Add native vector column to NoteEmbedding
+-- Convert existing JSON-string embeddings to native vector(1536)
+ALTER TABLE "NoteEmbedding" ADD COLUMN "vec" vector(1536);
+
+-- Migrate existing data: parse JSON arrays into pgvector format
+UPDATE "NoteEmbedding"
+SET "vec" = ("embedding"::jsonb)::text::vector(1536)
+WHERE "embedding" IS NOT NULL;
+
+-- Drop old string column, rename new one
+ALTER TABLE "NoteEmbedding" DROP COLUMN "embedding";
+ALTER TABLE "NoteEmbedding" RENAME COLUMN "vec" TO "embedding";
+
+-- Add updatedAt column for tracking reindex freshness
+ALTER TABLE "NoteEmbedding" ADD COLUMN "updatedAt" TIMESTAMP NOT NULL DEFAULT now();
+
+-- HNSW index for fast approximate nearest neighbor search (cosine distance)
+CREATE INDEX "NoteEmbedding_embedding_hnsw_idx" ON "NoteEmbedding"
+  USING hnsw ("embedding" vector_cosine_ops)
+  WITH (m = 16, ef_construction = 64);
+
+-- Phase 3: Add full-text search tsvector column to Note
+ALTER TABLE "Note" ADD COLUMN "tsv" tsvector;
+
+-- Populate tsv from existing title + content
+UPDATE "Note"
+SET "tsv" =
+  setweight(to_tsvector('simple', COALESCE("title", '')), 'A') ||
+  setweight(to_tsvector('simple', COALESCE("content", '')), 'B');
+
+-- GIN index for fast FTS queries
+CREATE INDEX "Note_tsv_gin_idx" ON "Note" USING gin ("tsv");
+
+-- Trigger function to auto-update tsv on INSERT or UPDATE of title/content
+CREATE OR REPLACE FUNCTION "note_tsv_trigger"() RETURNS trigger AS $$
+BEGIN
+  NEW."tsv" :=
+    setweight(to_tsvector('simple', COALESCE(NEW."title", '')), 'A') ||
+    setweight(to_tsvector('simple', COALESCE(NEW."content", '')), 'B');
+  RETURN NEW;
+END;
+$$ LANGUAGE plpgsql;
+
+-- Attach trigger
+DROP TRIGGER IF EXISTS "note_tsv_update" ON "Note";
+CREATE TRIGGER "note_tsv_update"
+  BEFORE INSERT OR UPDATE OF "title", "content" ON "Note"
+  FOR EACH ROW
+  EXECUTE FUNCTION "note_tsv_trigger"();

memento-note/prisma/schema.prisma

@@ -155,6 +155,7 @@ model Note {
   languageConfidence  Float?
   lastAiAnalysis      DateTime?
   trashedAt           DateTime?
+  tsv                 Unsupported("tsvector")?
   aiFeedback          AiFeedback[]
   memoryEchoAsNote1   MemoryEchoInsight[] @relation("EchoNote1")
   memoryEchoAsNote2   MemoryEchoInsight[] @relation("EchoNote2")
@@ -299,8 +300,9 @@ model UserAISettings {
 model NoteEmbedding {
   id        String   @id @default(cuid())
   noteId    String   @unique
-  embedding String
+  embedding Unsupported("vector(1536)")
   createdAt DateTime @default(now())
+  updatedAt DateTime @updatedAt
   note      Note     @relation(fields: [noteId], references: [id], onDelete: Cascade)
 
   @@index([noteId])