feat(api): Hono backend skeleton with /health endpoint and test

apps/api/package.json

@@ -0,0 +1,30 @@
+{
+  "name": "@solelog/api",
+  "version": "0.0.0",
+  "private": true,
+  "type": "module",
+  "scripts": {
+    "dev": "tsx watch src/index.ts",
+    "start": "tsx src/index.ts",
+    "test": "vitest run",
+    "test:watch": "vitest",
+    "typecheck": "tsc --noEmit",
+    "db:generate": "drizzle-kit generate",
+    "db:migrate": "tsx src/db/migrate.ts"
+  },
+  "dependencies": {
+    "@hono/node-server": "^1.13.7",
+    "@libsql/client": "^0.14.0",
+    "@solelog/shared": "workspace:*",
+    "better-auth": "^1.1.7",
+    "drizzle-orm": "^0.36.4",
+    "hono": "^4.6.14",
+    "zod": "^3.23.8"
+  },
+  "devDependencies": {
+    "drizzle-kit": "^0.30.1",
+    "tsx": "^4.19.2",
+    "typescript": "^5.7.2",
+    "vitest": "^3.0.0"
+  }
+}