refactor: enforce strict backend typing

Enable strict TypeScript and reject non-null and definite-assignment assertions. Declare externally populated DTO fields, preserve runtime validation, and narrow values at their owners.

Verified: backend verify (257 tests), unchanged OpenAPI, and 21 SQLite/HTTP tests on retry. The initial SQLite run had two timeouts; baseline HEAD passed 21 tests as well.

tsconfig.json

@@ -16,10 +16,8 @@
     "baseUrl": "./",
     "incremental": true,
     "skipLibCheck": true,
-    "strictNullChecks": true,
+    "strict": true,
     "forceConsistentCasingInFileNames": true,
-    "noImplicitAny": false,
-    "strictBindCallApply": false,
-    "noFallthroughCasesInSwitch": false
+    "noFallthroughCasesInSwitch": true
   }
 }