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/lib/ai/services/memory-echo.service.ts

@@ -1,5 +1,6 @@
 import { getAIProvider, getChatProvider } from '../factory'
 import { cosineSimilarity } from '@/lib/utils'
+import { embeddingService } from './embedding.service'
 import { getSystemConfig } from '@/lib/config'
 import prisma from '@/lib/prisma'
 
@@ -78,11 +79,15 @@ export class MemoryEchoService {
         try {
           const embedding = await provider.getEmbeddings(note.content)
           if (embedding && embedding.length > 0) {
-            await prisma.noteEmbedding.upsert({
-              where: { noteId: note.id },
-              create: { noteId: note.id, embedding: JSON.stringify(embedding) },
-              update: { embedding: JSON.stringify(embedding) }
-            })
+            const vecStr = `[${embedding.join(',')}]`
+            await prisma.$executeRawUnsafe(
+              `INSERT INTO "NoteEmbedding" ("id", "noteId", "embedding", "createdAt", "updatedAt")
+               VALUES (gen_random_uuid(), $1, $2::vector, now(), now())
+               ON CONFLICT ("noteId")
+               DO UPDATE SET "embedding" = $2::vector, "updatedAt" = now()`,
+              note.id,
+              vecStr
+            )
           }
         } catch {
           // Skip this note, continue with others
@@ -122,11 +127,12 @@ export class MemoryEchoService {
       return [] // Need at least 2 notes to find connections
     }
 
-    // Parse embeddings (already native Json from PostgreSQL)
     const notesWithEmbeddings = notes
       .map(note => ({
         ...note,
-        embedding: note.noteEmbedding?.embedding ? JSON.parse(note.noteEmbedding.embedding) as number[] : null
+        embedding: note.noteEmbedding?.embedding
+          ? embeddingService.fromVectorString(note.noteEmbedding.embedding as unknown as string)
+          : null
       }))
       .filter(note => note.embedding && Array.isArray(note.embedding))
 
@@ -500,8 +506,9 @@ Explain in one brief sentence (max 15 words) why these notes are connected. Focu
       return []
     }
 
-    // Target note embedding (already native Json from PostgreSQL)
-    const targetEmbedding = targetNote.noteEmbedding?.embedding ? JSON.parse(targetNote.noteEmbedding.embedding) as number[] : null
+    const targetEmbedding = targetNote.noteEmbedding?.embedding
+      ? embeddingService.fromVectorString(targetNote.noteEmbedding.embedding as unknown as string)
+      : null
     if (!targetEmbedding) return []
 
     // Check if user has demo mode enabled
@@ -535,7 +542,9 @@ Explain in one brief sentence (max 15 words) why these notes are connected. Focu
     for (const otherNote of otherNotes) {
       if (!otherNote.noteEmbedding) continue
 
-      const otherEmbedding = otherNote.noteEmbedding?.embedding ? JSON.parse(otherNote.noteEmbedding.embedding) as number[] : null
+      const otherEmbedding = otherNote.noteEmbedding?.embedding
+        ? embeddingService.fromVectorString(otherNote.noteEmbedding.embedding as unknown as string)
+        : null
       if (!otherEmbedding) continue
 
       // Check if this connection was dismissed