feat(14-01): rewrite database foundation from SQLite to PostgreSQL

- Replace all 13 sqliteTable definitions with pgTable (pg-core)
- Convert integer timestamps to native timestamp type with defaultNow()
- Convert real columns to doublePrecision, integer used to boolean
- Rewrite db connection to use postgres.js driver with DATABASE_URL
- Rewrite migrate.ts to use postgres-js migrator targeting drizzle-pg/
- Convert seed.ts to async
- Update drizzle.config.ts to postgresql dialect
- Install postgres and @electric-sql/pglite, remove better-sqlite3

bun.lock

@@ -5,6 +5,7 @@
     "": {
       "name": "gearbox",
       "dependencies": {
+        "@electric-sql/pglite": "^0.4.3",
         "@hono/zod-validator": "^0.7.6",
         "@modelcontextprotocol/sdk": "^1.29.0",
         "@tailwindcss/vite": "^4.2.1",
@@ -15,6 +16,7 @@
         "framer-motion": "^12.38.0",
         "hono": "^4.12.8",
         "lucide-react": "^0.577.0",
+        "postgres": "^3.4.8",
         "react": "^19.2.4",
         "react-dom": "^19.2.4",
         "recharts": "^3.8.0",
@@ -28,12 +30,10 @@
         "@tanstack/react-query-devtools": "^5.91.3",
         "@tanstack/react-router-devtools": "^1.166.7",
         "@tanstack/router-plugin": "^1.166.9",
-        "@types/better-sqlite3": "^7.6.13",
         "@types/bun": "latest",
         "@types/react": "^19.2.14",
         "@types/react-dom": "^19.2.3",
         "@vitejs/plugin-react": "^6.0.1",
-        "better-sqlite3": "^12.8.0",
         "concurrently": "^9.1.2",
         "drizzle-kit": "^0.31.9",
         "vite": "^8.0.0",
@@ -102,6 +102,8 @@
 
     "@drizzle-team/brocli": ["@drizzle-team/brocli@0.10.2", "", {}, "sha512-z33Il7l5dKjUgGULTqBsQBQwckHh5AbIuxhdsIxDDiZAzBOrZO6q9ogcWC65kU382AfynTfgNumVcNIjuIua6w=="],
 
+    "@electric-sql/pglite": ["@electric-sql/pglite@0.4.3", "", {}, "sha512-ichuWTgtd4mOM1G4SpyGJa5trT03lWbMypDV0fUXUCXg5hiHqVAz/bZyV68NqmkLB7WcYmj1RMJVSp8HV/v/ZQ=="],
+
     "@emnapi/core": ["@emnapi/core@1.9.0", "", { "dependencies": { "@emnapi/wasi-threads": "1.2.0", "tslib": "^2.4.0" } }, "sha512-0DQ98G9ZQZOxfUcQn1waV2yS8aWdZ6kJMbYCJB3oUBecjWYO1fqJ+a1DRfPF3O5JEkwqwP1A9QEN/9mYm2Yd0w=="],
 
     "@emnapi/runtime": ["@emnapi/runtime@1.9.0", "", { "dependencies": { "tslib": "^2.4.0" } }, "sha512-QN75eB0IH2ywSpRpNddCRfQIhmJYBCJ1x5Lb3IscKAL8bMnVAKnRg8dCoXbHzVLLH7P38N2Z3mtulB7W0J0FKw=="],
@@ -684,6 +686,8 @@
 
     "postcss": ["postcss@8.5.8", "", { "dependencies": { "nanoid": "^3.3.11", "picocolors": "^1.1.1", "source-map-js": "^1.2.1" } }, "sha512-OW/rX8O/jXnm82Ey1k44pObPtdblfiuWnrd8X7GJ7emImCOstunGbXUpp7HdBrFQX6rJzn3sPT397Wp5aCwCHg=="],
 
+    "postgres": ["postgres@3.4.8", "", {}, "sha512-d+JFcLM17njZaOLkv6SCev7uoLaBtfK86vMUXhW1Z4glPWh4jozno9APvW/XKFJ3CCxVoC7OL38BqRydtu5nGg=="],
+
     "prebuild-install": ["prebuild-install@7.1.3", "", { "dependencies": { "detect-libc": "^2.0.0", "expand-template": "^2.0.3", "github-from-package": "0.0.0", "minimist": "^1.2.3", "mkdirp-classic": "^0.5.3", "napi-build-utils": "^2.0.0", "node-abi": "^3.3.0", "pump": "^3.0.0", "rc": "^1.2.7", "simple-get": "^4.0.0", "tar-fs": "^2.0.0", "tunnel-agent": "^0.6.0" }, "bin": { "prebuild-install": "bin.js" } }, "sha512-8Mf2cbV7x1cXPUILADGI3wuhfqWvtiLA1iclTDbFRZkgRQS0NqsPZphna9V+HyTEadheuPmjaJMsbzKQFOzLug=="],
 
     "prettier": ["prettier@3.8.1", "", { "bin": { "prettier": "bin/prettier.cjs" } }, "sha512-UOnG6LftzbdaHZcKoPFtOcCKztrQ57WkHDeRD9t/PTQtmT0NHSeWWepj6pS0z/N7+08BHFDQVUrfmfMRcZwbMg=="],