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.

src/common/money.dto.ts

@@ -2,8 +2,8 @@ import { ApiProperty } from '@nestjs/swagger';
 
 export class MoneyDto {
   @ApiProperty()
-  currency: string;
+  declare currency: string;
 
   @ApiProperty()
-  value: string;
+  declare value: string;
 }