feat: adopt bchen-sqlite-migrate package; replace inline SCHEMA_DDL

Phase 3 of the cross-project sqlite-migrate adoption — port nanodrop to
consume bchen-sqlite-migrate@v0.1.0. Replaces the inline db.exec(...)
block in src/db/schema.ts with applyMigrations(db, MIGRATIONS_DIR,
{ genesisProbeTable: 'users' }).

The genesis-probe (table 'users' exists) handles pre-existing prod DBs
automatically — first deploy after merge stamps 0001_init as applied
without re-executing, subsequent boots are no-ops.

Adds three npm scripts (db:migrate, db:status, db:stamp) and a
byte-stability test pinning sha256(0001_init.sql) so the migration is
treated as immutable history.

package.json

@@ -9,7 +9,10 @@
     "dev": "tsx src/index.ts",
     "test": "vitest run",
     "test:watch": "vitest",
-    "register-user": "tsx src/cli/register-user.ts"
+    "register-user": "tsx src/cli/register-user.ts",
+    "db:migrate": "tsx src/scripts/db-migrate.ts",
+    "db:status": "tsx src/scripts/db-status.ts",
+    "db:stamp": "tsx src/scripts/db-stamp.ts"
   },
   "author": "",
   "license": "ISC",
@@ -20,6 +23,7 @@
     "@fastify/multipart": "^9.4.0",
     "@fastify/rate-limit": "^10.3.0",
     "@fastify/static": "^9.0.0",
+    "bchen-sqlite-migrate": "git+https://gitea.bchen.dev/brendan/sqlite-migrate.git#v0.1.0",
     "bcrypt": "^6.0.0",
     "better-sqlite3": "^12.6.2",
     "fastify": "^5.7.4",